Grafik Persamaan Fungsi Trigonometri

Fungsi f dengan wilayah R dikatakan periodik apabila ada bilangan  alt="p \ne 0" src="https://s0.wp.com/latex.php?latex=p+%5Cne+0&bg=f9f9f9&fg=000000&s=0" title="p \ne 0" />, sedemikian sehingga  alt="f(x+p) = f(x)" src="https://s0.wp.com/latex.php?latex=f%28x%2Bp%29+%3D+f%28x%29&bg=f9f9f9&fg=000000&s=0" title="f(x+p) = f(x)" />, dengan  alt="x \epsilon R" src="https://s0.wp.com/latex.php?latex=x+%5Cepsilon+R&bg=f9f9f9&fg=000000&s=0" title="x \epsilon R" />. Bilangan positif p terkecil yang memenuhi  alt="f(x+p) = f(x)" src="https://s0.wp.com/latex.php?latex=f%28x%2Bp%29+%3D+f%28x%29&bg=f9f9f9&fg=000000&s=0" title="f(x+p) = f(x)" /> disebut periode dasar fungsi f.

Jika fungsi f periodik dengan periode dasar p, maka periode-periode dari fungsi f adalah  alt="n \times p" src="https://s0.wp.com/latex.php?latex=n+%5Ctimes+p&bg=f9f9f9&fg=000000&s=0" title="n \times p" />, dengan n adalah bilangan asli. Jika f dan g adalah fungsi yang periodik dengan periode p, maka  alt="f+g" src="https://s0.wp.com/latex.php?latex=f%2Bg&bg=f9f9f9&fg=000000&s=0" title="f+g" /> dan fg juga periodik dengan periode p.

1. Periode fungsi sinus dan kosinus

Untuk penambahan panjang busur  alt="a" src="https://s0.wp.com/latex.php?latex=a&bg=f9f9f9&fg=000000&s=0" title="a" /> dengan kelipatan  alt="2\pi" src="https://s0.wp.com/latex.php?latex=2%5Cpi&bg=f9f9f9&fg=000000&s=0" title="2\pi" /> (satu putran penuh) akan diperoleh titik p(a) yang sama, sehingga secara umum berlaku :

• alt="\sin (a+k \times 2\pi) = \sin a" src="https://s0.wp.com/latex.php?latex=%5Csin+%28a%2Bk+%5Ctimes+2%5Cpi%29+%3D+%5Csin+a&bg=f9f9f9&fg=000000&s=0" title="\sin (a+k \times 2\pi) = \sin a" /> dengan k∈B atau
• alt="\sin (a+k\times 360^{\circ}) = \sin a^{\circ}" src="https://s0.wp.com/latex.php?latex=%5Csin+%28a%2Bk%5Ctimes+360%5E%7B%5Ccirc%7D%29+%3D+%5Csin+a%5E%7B%5Ccirc%7D&bg=f9f9f9&fg=000000&s=0" title="\sin (a+k\times 360^{\circ}) = \sin a^{\circ}" /> dengan k∈B
• alt="\cos (a+k\times 2\pi)" src="https://s0.wp.com/latex.php?latex=%5Ccos+%28a%2Bk%5Ctimes+2%5Cpi%29&bg=f9f9f9&fg=000000&s=0" title="\cos (a+k\times 2\pi)" /> dengan k∈B atau
• alt="\cos (a+ k\times 360^{\circ})" src="https://s0.wp.com/latex.php?latex=%5Ccos+%28a%2B+k%5Ctimes+360%5E%7B%5Ccirc%7D%29&bg=f9f9f9&fg=000000&s=0" title="\cos (a+ k\times 360^{\circ})" /> dengan k∈B

Dengan demikian, fungsi sinus  alt="f(x) = \sin x" src="https://s0.wp.com/latex.php?latex=f%28x%29+%3D+%5Csin+x&bg=f9f9f9&fg=000000&s=0" title="f(x) = \sin x" />vatau  alt="f(x) = \sin x^{\circ}" src="https://s0.wp.com/latex.php?latex=f%28x%29+%3D+%5Csin+x%5E%7B%5Ccirc%7D&bg=f9f9f9&fg=000000&s=0" title="f(x) = \sin x^{\circ}" /> dan fungsi kosinus  alt="f(x) = cos x" src="https://s0.wp.com/latex.php?latex=f%28x%29+%3D+cos+x&bg=f9f9f9&fg=000000&s=0" title="f(x) = cos x" /> atau  alt="f(x) = cos x^{\circ}" src="https://s0.wp.com/latex.php?latex=f%28x%29+%3D+cos+x%5E%7B%5Ccirc%7D&bg=f9f9f9&fg=000000&s=0" title="f(x) = cos x^{\circ}" /> adalah fungsi periodik dengan periode dasar  alt="2\pi" src="https://s0.wp.com/latex.php?latex=2%5Cpi&bg=f9f9f9&fg=000000&s=0" title="2\pi" />atau  alt="360^{\circ}" src="https://s0.wp.com/latex.php?latex=360%5E%7B%5Ccirc%7D&bg=f9f9f9&fg=000000&s=0" title="360^{\circ}" />.

alt="" src="https://cdn.utakatikotak.com/finder/grafik-fungsi-trigonometri-sinus-dan-cosinus.png" style="height:296px; width:307px" />

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Pengertian Trigonometri dan Rumus Trigonometri Lengkap dengan Soal

Perbandingan Trigonometri dan Tabel Trigonometri Lengkap

2. Periode fungsi tangen

Untuk penambahan panjang busur  alt="a" src="https://s0.wp.com/latex.php?latex=a&bg=f9f9f9&fg=000000&s=0" title="a" /> dengan kelipatan  alt="\pi" src="https://s0.wp.com/latex.php?latex=%5Cpi&bg=f9f9f9&fg=000000&s=0" title="\pi" /> (setengah putran penuh) akan diperoleh titik  alt="p(a+k\times p)" src="https://s0.wp.com/latex.php?latex=p%28a%2Bk%5Ctimes+p%29&bg=f9f9f9&fg=000000&s=0" title="p(a+k\times p)" /> yang nilai tangennya sama untuk kedua sudut tersebut, sehingga secara umum  alt="\tan (a + k \times \pi) = \tan a" src="https://s0.wp.com/latex.php?latex=%5Ctan+%28a+%2B+k+%5Ctimes+%5Cpi%29+%3D+%5Ctan+a&bg=f9f9f9&fg=000000&s=0" title="\tan (a + k \times \pi) = \tan a" /> dengan  alt="k \epsilon B" src="https://s0.wp.com/latex.php?latex=k+%5Cepsilon+B&bg=f9f9f9&fg=000000&s=0" title="k \epsilon B" /> atau  alt="\tan (a+k\times 1806{\circ}) = \tan a^{\circ}" src="https://s0.wp.com/latex.php?latex=%5Ctan+%28a%2Bk%5Ctimes+1806%7B%5Ccirc%7D%29+%3D+%5Ctan+a%5E%7B%5Ccirc%7D&bg=f9f9f9&fg=000000&s=0" title="\tan (a+k\times 1806{\circ}) = \tan a^{\circ}" /> dengan  alt="k \epsilon B" src="https://s0.wp.com/latex.php?latex=k+%5Cepsilon+B&bg=f9f9f9&fg=000000&s=0" title="k \epsilon B" />.

alt="" src="https://cdn.utakatikotak.com/finder/grafik-fungsi-tangen.png" style="height:307px; width:295px" />

Dengan demikian tangen  alt="f(x) = \tan x" src="https://s0.wp.com/latex.php?latex=f%28x%29+%3D+%5Ctan+x&bg=f9f9f9&fg=000000&s=0" title="f(x) = \tan x" /> atau  alt="f(x) = \tan^{\circ}" src="https://s0.wp.com/latex.php?latex=f%28x%29+%3D+%5Ctan%5E%7B%5Ccirc%7D&bg=f9f9f9&fg=000000&s=0" title="f(x) = \tan^{\circ}" /> adalah fungsi periodik dengan periode  alt=" \pi" src="https://s0.wp.com/latex.php?latex=+%5Cpi&bg=f9f9f9&fg=000000&s=0" title=" \pi" /> atau  alt="180^{\circ}" src="https://s0.wp.com/latex.php?latex=180%5E%7B%5Ccirc%7D&bg=f9f9f9&fg=000000&s=0" title="180^{\circ}" />.

Grafik Fungsi Trigonometri

alt="" src="https://cdn.utakatikotak.com/finder/grafik-fungsi-trigonometri-lengkap.png" style="height:279px; width:624px" />

Dengan td adalah tidak didefinisikan. Untuk memudahkan, maka lihatlah segitiga berikut :

alt="" src="https://cdn.utakatikotak.com/finder/sudut-istimewa-segitiga.png" style="height:321px; width:275px" />

Dari konsep segitiga tersebut diperoleh nilai setiap sudut  alt="30^{\circ}, 45^{\circ} " src="https://s0.wp.com/latex.php?latex=30%5E%7B%5Ccirc%7D%2C+45%5E%7B%5Ccirc%7D+&bg=f9f9f9&fg=000000&s=0" title="30^{\circ}, 45^{\circ} " /> dan  alt="60^{\circ} " src="https://s0.wp.com/latex.php?latex=60%5E%7B%5Ccirc%7D+&bg=f9f9f9&fg=000000&s=0" title="60^{\circ} " />. Untuk sudut  alt="0^{\circ} " src="https://s0.wp.com/latex.php?latex=0%5E%7B%5Ccirc%7D+&bg=f9f9f9&fg=000000&s=0" title="0^{\circ} " /> dan  alt="90^{\circ} " src="https://s0.wp.com/latex.php?latex=90%5E%7B%5Ccirc%7D+&bg=f9f9f9&fg=000000&s=0" title="90^{\circ} " /> diperoleh dengan cara berikut :

alt="" src="https://cdn.utakatikotak.com/finder/konsep-segitiga-trigonometri.png" style="height:295px; width:310px" />

Didapat :

• alt="\sin a = \frac{y}{r}" src="https://s0.wp.com/latex.php?latex=%5Csin+a+%3D+%5Cfrac%7By%7D%7Br%7D&bg=f9f9f9&fg=000000&s=0" title="\sin a = \frac{y}{r}" />
• alt="cos a = \frac{x}{r}" src="https://s0.wp.com/latex.php?latex=cos+a+%3D+%5Cfrac%7Bx%7D%7Br%7D&bg=f9f9f9&fg=000000&s=0" title="cos a = \frac{x}{r}" />
• alt="\tan a = \frac{y}{x}" src="https://s0.wp.com/latex.php?latex=%5Ctan+a+%3D+%5Cfrac%7By%7D%7Bx%7D&bg=f9f9f9&fg=000000&s=0" title="\tan a = \frac{y}{x}" />

Jika titik  alt="P(x,y)" src="https://s0.wp.com/latex.php?latex=P%28x%2Cy%29&bg=f9f9f9&fg=000000&s=0" title="P(x,y)" />bergerak mendekati sumbu X positif, akhirnya berimpit dengan sumbu X, maka x=r, y=0,  alt=" x = r,y = 0" src="https://s0.wp.com/latex.php?latex=+x+%3D+r%2Cy+%3D+0&bg=f9f9f9&fg=000000&s=0" title=" x = r,y = 0" /> dan  alt="a^{\circ} =0^{\circ}" src="https://s0.wp.com/latex.php?latex=a%5E%7B%5Ccirc%7D+%3D0%5E%7B%5Ccirc%7D&bg=f9f9f9&fg=000000&s=0" title="a^{\circ} =0^{\circ}" />, sehingga

• alt="\sin 0^{\circ} = \frac{0}{r} = 0" src="https://s0.wp.com/latex.php?latex=%5Csin+0%5E%7B%5Ccirc%7D+%3D+%5Cfrac%7B0%7D%7Br%7D+%3D+0&bg=f9f9f9&fg=000000&s=0" title="\sin 0^{\circ} = \frac{0}{r} = 0" />
• alt="\cos 0^{\circ} = \frac{r}{r} = 1" src="https://s0.wp.com/latex.php?latex=%5Ccos+0%5E%7B%5Ccirc%7D+%3D+%5Cfrac%7Br%7D%7Br%7D+%3D+1&bg=f9f9f9&fg=000000&s=0" title="\cos 0^{\circ} = \frac{r}{r} = 1" />
• alt="\tan 0^{\circ} = \frac{0}{r} = 0" src="https://s0.wp.com/latex.php?latex=%5Ctan+0%5E%7B%5Ccirc%7D+%3D+%5Cfrac%7B0%7D%7Br%7D+%3D+0&bg=f9f9f9&fg=000000&s=0" title="\tan 0^{\circ} = \frac{0}{r} = 0" />

Jika titik P(x,y) alt="P(x,y)" src="https://s0.wp.com/latex.php?latex=P%28x%2Cy%29&bg=f9f9f9&fg=000000&s=0" title="P(x,y)" />bergerak mendekati sumbu Y positif, akhirnya berimpit dengan sumbu Y, maka

alt="x =0,y = r" src="https://s0.wp.com/latex.php?latex=x+%3D0%2Cy+%3D+r&bg=f9f9f9&fg=000000&s=0" title="x =0,y = r" />, dan  alt="a^{\circ} = 90^{\circ}" src="https://s0.wp.com/latex.php?latex=a%5E%7B%5Ccirc%7D+%3D+90%5E%7B%5Ccirc%7D&bg=f9f9f9&fg=000000&s=0" title="a^{\circ} = 90^{\circ}" />, sehingga

• alt="\sin 90^{\circ} = \frac{r}{r} = 1" src="https://s0.wp.com/latex.php?latex=%5Csin+90%5E%7B%5Ccirc%7D+%3D+%5Cfrac%7Br%7D%7Br%7D+%3D+1&bg=f9f9f9&fg=000000&s=0" title="\sin 90^{\circ} = \frac{r}{r} = 1" />
• alt="\cos 0^{\circ} = \frac{0}{r} = 0" src="https://s0.wp.com/latex.php?latex=%5Ccos+0%5E%7B%5Ccirc%7D+%3D+%5Cfrac%7B0%7D%7Br%7D+%3D+0&bg=f9f9f9&fg=000000&s=0" title="\cos 0^{\circ} = \frac{0}{r} = 0" />
• tan⁡  alt="\tan 0^{\circ} = \frac{r}{0}" src="https://s0.wp.com/latex.php?latex=%5Ctan+0%5E%7B%5Ccirc%7D+%3D+%5Cfrac%7Br%7D%7B0%7D&bg=f9f9f9&fg=000000&s=0" title="\tan 0^{\circ} = \frac{r}{0}" /> = tidak didefinisikan

Nilai Maksimum dan Minimum Fungsi Trigonometri

Untuk setiap titik P(x,y) alt="P(x,y)" src="https://s0.wp.com/latex.php?latex=P%28x%2Cy%29&bg=f9f9f9&fg=000000&s=0" title="P(x,y)" /> pada fungsi trigonometri memiliki hubungan :

• alt="-r \le x \le r" src="https://s0.wp.com/latex.php?latex=-r+%5Cle+x+%5Cle+r&bg=f9f9f9&fg=000000&s=0" title="-r \le x \le r" /> dan  alt="-r \le y \le r" src="https://s0.wp.com/latex.php?latex=-r+%5Cle+y+%5Cle+r&bg=f9f9f9&fg=000000&s=0" title="-r \le y \le r" />
• alt="-1 \le \frac{x}{r} \le 1" src="https://s0.wp.com/latex.php?latex=-1+%5Cle+%5Cfrac%7Bx%7D%7Br%7D+%5Cle+1&bg=f9f9f9&fg=000000&s=0" title="-1 \le \frac{x}{r} \le 1" /> dan  alt="-1 \le \frac{y}{r} \le 1" src="https://s0.wp.com/latex.php?latex=-1+%5Cle+%5Cfrac%7By%7D%7Br%7D+%5Cle+1&bg=f9f9f9&fg=000000&s=0" title="-1 \le \frac{y}{r} \le 1" />
• alt="-1 \le \cos a \le 1" src="https://s0.wp.com/latex.php?latex=-1+%5Cle+%5Ccos+a+%5Cle+1&bg=f9f9f9&fg=000000&s=0" title="-1 \le \cos a \le 1" /> dan  alt="-1 \le \sin a \le 1" src="https://s0.wp.com/latex.php?latex=-1+%5Cle+%5Csin+a+%5Cle+1&bg=f9f9f9&fg=000000&s=0" title="-1 \le \sin a \le 1" />

Berdasarkan uraian tersebut dapat dikemukakan bahwa :

Nilai maksimum dan minimum fungsi sinus

• Fungsi sinus  alt="y =f(x) = \sin x" src="https://s0.wp.com/latex.php?latex=y+%3Df%28x%29+%3D+%5Csin+x&bg=f9f9f9&fg=000000&s=0" title="y =f(x) = \sin x" /> memiliki nilai maksimum  alt="y_{maks} = 1" src="https://s0.wp.com/latex.php?latex=y_%7Bmaks%7D+%3D+1&bg=f9f9f9&fg=000000&s=0" title="y_{maks} = 1" /> yang dicapai untuk  alt="x =\frac{1}{2}\pi + k \times 2\pi" src="https://s0.wp.com/latex.php?latex=x+%3D%5Cfrac%7B1%7D%7B2%7D%5Cpi+%2B+k+%5Ctimes+2%5Cpi&bg=f9f9f9&fg=000000&s=0" title="x =\frac{1}{2}\pi + k \times 2\pi" /> dengan  alt="k \epsilon B" src="https://s0.wp.com/latex.php?latex=k+%5Cepsilon+B&bg=f9f9f9&fg=000000&s=0" title="k \epsilon B" /> dan nilai minimum  alt="y_{min} = -1" src="https://s0.wp.com/latex.php?latex=y_%7Bmin%7D+%3D+-1&bg=f9f9f9&fg=000000&s=0" title="y_{min} = -1" /> yang dicapai untuk  alt="x = \frac{3}{2}\pi + k \times 2\pi" src="https://s0.wp.com/latex.php?latex=x+%3D+%5Cfrac%7B3%7D%7B2%7D%5Cpi+%2B+k+%5Ctimes+2%5Cpi&bg=f9f9f9&fg=000000&s=0" title="x = \frac{3}{2}\pi + k \times 2\pi" /> dengan  alt="k \epsilon B" src="https://s0.wp.com/latex.php?latex=k+%5Cepsilon+B&bg=f9f9f9&fg=000000&s=0" title="k \epsilon B" />.
• Fungsi sinus  alt="y = f(x) = \sin x^{\circ}" src="https://s0.wp.com/latex.php?latex=y+%3D+f%28x%29+%3D+%5Csin+x%5E%7B%5Ccirc%7D&bg=f9f9f9&fg=000000&s=0" title="y = f(x) = \sin x^{\circ}" /> memiliki nilai maksimum  alt="y_{maks} = 1" src="https://s0.wp.com/latex.php?latex=y_%7Bmaks%7D+%3D+1&bg=f9f9f9&fg=000000&s=0" title="y_{maks} = 1" /> yang dicapai untuk  alt="x = 90^{\circ} + k \times 360^{\circ}" src="https://s0.wp.com/latex.php?latex=x+%3D+90%5E%7B%5Ccirc%7D+%2B+k+%5Ctimes+360%5E%7B%5Ccirc%7D&bg=f9f9f9&fg=000000&s=0" title="x = 90^{\circ} + k \times 360^{\circ}" /> dengan  alt="k \epsilon B" src="https://s0.wp.com/latex.php?latex=k+%5Cepsilon+B&bg=f9f9f9&fg=000000&s=0" title="k \epsilon B" /> dan nilai minimum  alt="y_{maks} = -1" src="https://s0.wp.com/latex.php?latex=y_%7Bmaks%7D+%3D+-1&bg=f9f9f9&fg=000000&s=0" title="y_{maks} = -1" />yang dicapai untuk  alt="x = 270^{\circ} + k \times 360^{\circ}" src="https://s0.wp.com/latex.php?latex=x+%3D+270%5E%7B%5Ccirc%7D+%2B+k+%5Ctimes+360%5E%7B%5Ccirc%7D&bg=f9f9f9&fg=000000&s=0" title="x = 270^{\circ} + k \times 360^{\circ}" />dengan  alt="k \epsilon B" src="https://s0.wp.com/latex.php?latex=k+%5Cepsilon+B&bg=f9f9f9&fg=000000&s=0" title="k \epsilon B" />.

Nilai maksimum dan minimum fungsi kosinus

• Fungsi kosinus  alt="y = f(x) = \cos x" src="https://s0.wp.com/latex.php?latex=y+%3D+f%28x%29+%3D+%5Ccos+x&bg=f9f9f9&fg=000000&s=0" title="y = f(x) = \cos x" /> memiliki nilai maksimum  alt="y_{maks} = 1" src="https://s0.wp.com/latex.php?latex=y_%7Bmaks%7D+%3D+1&bg=f9f9f9&fg=000000&s=0" title="y_{maks} = 1" /> yang dicapai untuk  alt="x =k \times 2\pi" src="https://s0.wp.com/latex.php?latex=x+%3Dk+%5Ctimes+2%5Cpi&bg=f9f9f9&fg=000000&s=0" title="x =k \times 2\pi" /> dengan  alt="k \epsilon B" src="https://s0.wp.com/latex.php?latex=k+%5Cepsilon+B&bg=f9f9f9&fg=000000&s=0" title="k \epsilon B" /> dan nilai minimum  alt="y_{min} = -1" src="https://s0.wp.com/latex.php?latex=y_%7Bmin%7D+%3D+-1&bg=f9f9f9&fg=000000&s=0" title="y_{min} = -1" /> yang dicapai untuk  alt="x = \pi + k \times 2\pi" src="https://s0.wp.com/latex.php?latex=x+%3D+%5Cpi+%2B+k+%5Ctimes+2%5Cpi&bg=f9f9f9&fg=000000&s=0" title="x = \pi + k \times 2\pi" /> dengan  alt="k \epsilon B" src="https://s0.wp.com/latex.php?latex=k+%5Cepsilon+B&bg=f9f9f9&fg=000000&s=0" title="k \epsilon B" />.
• Fungsi kosinus  alt="y = f(x) = \cos x^{\circ}" src="https://s0.wp.com/latex.php?latex=y+%3D+f%28x%29+%3D+%5Ccos+x%5E%7B%5Ccirc%7D&bg=f9f9f9&fg=000000&s=0" title="y = f(x) = \cos x^{\circ}" /> memiliki nilai maksimum  alt="y_{maks} = 1" src="https://s0.wp.com/latex.php?latex=y_%7Bmaks%7D+%3D+1&bg=f9f9f9&fg=000000&s=0" title="y_{maks} = 1" /> yang dicapai untuk  alt="x = k \times 360^{\circ}" src="https://s0.wp.com/latex.php?latex=x+%3D+k+%5Ctimes+360%5E%7B%5Ccirc%7D&bg=f9f9f9&fg=000000&s=0" title="x = k \times 360^{\circ}" /> dengan  alt="k \epsilon B" src="https://s0.wp.com/latex.php?latex=k+%5Cepsilon+B&bg=f9f9f9&fg=000000&s=0" title="k \epsilon B" /> dan nilai minimum  alt="y_{min} = -1" src="https://s0.wp.com/latex.php?latex=y_%7Bmin%7D+%3D+-1&bg=f9f9f9&fg=000000&s=0" title="y_{min} = -1" /> yang dicapai untuk  alt="x = 180^{\circ} + k \times 360^{\circ}" src="https://s0.wp.com/latex.php?latex=x+%3D+180%5E%7B%5Ccirc%7D+%2B+k+%5Ctimes+360%5E%7B%5Ccirc%7D&bg=f9f9f9&fg=000000&s=0" title="x = 180^{\circ} + k \times 360^{\circ}" /> dengan  alt="k \epsilon B" src="https://s0.wp.com/latex.php?latex=k+%5Cepsilon+B&bg=f9f9f9&fg=000000&s=0" title="k \epsilon B" />.

Secara umum dapat dikemukakan bahwa :

1. Jika fungsi sinus  alt="y = f(x) = a \sin (bx + c) + d" src="https://s0.wp.com/latex.php?latex=y+%3D+f%28x%29+%3D+a+%5Csin+%28bx+%2B+c%29+%2B+d&bg=f9f9f9&fg=000000&s=0" title="y = f(x) = a \sin (bx + c) + d" />, maka nilai maksimumnya  alt="y_{maks} = \mid a\mid + d" src="https://s0.wp.com/latex.php?latex=y_%7Bmaks%7D+%3D+%5Cmid+a%5Cmid+%2B+d&bg=f9f9f9&fg=000000&s=0" title="y_{maks} = \mid a\mid + d" /> dan nilai minimumnya  alt="y_{min} = -\mid a\mid + d" src="https://s0.wp.com/latex.php?latex=y_%7Bmin%7D+%3D+-%5Cmid+a%5Cmid+%2B+d&bg=f9f9f9&fg=000000&s=0" title="y_{min} = -\mid a\mid + d" />
2. Jika fungsi kosinus  alt="y = f(x) = a \cos (bx + c) + d" src="https://s0.wp.com/latex.php?latex=y+%3D+f%28x%29+%3D+a+%5Ccos+%28bx+%2B+c%29+%2B+d&bg=f9f9f9&fg=000000&s=0" title="y = f(x) = a \cos (bx + c) + d" />, maka nilai maksimumnya  alt="y_{maks} = \mid a\mid + d" src="https://s0.wp.com/latex.php?latex=y_%7Bmaks%7D+%3D+%5Cmid+a%5Cmid+%2B+d&bg=f9f9f9&fg=000000&s=0" title="y_{maks} = \mid a\mid + d" /> dan nilai minimumnya  alt="y_{min} = -\mid a\mid + d" src="https://s0.wp.com/latex.php?latex=y_%7Bmin%7D+%3D+-%5Cmid+a%5Cmid+%2B+d&bg=f9f9f9&fg=000000&s=0" title="y_{min} = -\mid a\mid + d" />

3. Jika  alt="y = f(x)" src="https://s0.wp.com/latex.php?latex=y+%3D+f%28x%29&bg=f9f9f9&fg=000000&s=0" title="y = f(x)" /> adalah fungsi periodik dengan nilai maksimum  alt="y_{maks}" src="https://s0.wp.com/latex.php?latex=y_%7Bmaks%7D&bg=f9f9f9&fg=000000&s=0" title="y_{maks}" /> dan minimum  alt="y_{min}" src="https://s0.wp.com/latex.php?latex=y_%7Bmin%7D&bg=f9f9f9&fg=000000&s=0" title="y_{min}" />, maka amplitudonya adalah :

Jenis Grafik Fungsi Trigonometri

1. Grafik fungsi baku  alt="f(x) = \sin x" src="https://s0.wp.com/latex.php?latex=f%28x%29+%3D+%5Csin+x&bg=f9f9f9&fg=000000&s=0" title="f(x) = \sin x" />;  alt="f(x) = \cos x" src="https://s0.wp.com/latex.php?latex=f%28x%29+%3D+%5Ccos+x&bg=f9f9f9&fg=000000&s=0" title="f(x) = \cos x" />; dan  alt="f(x) = \tan x" src="https://s0.wp.com/latex.php?latex=f%28x%29+%3D+%5Ctan+x&bg=f9f9f9&fg=000000&s=0" title="f(x) = \tan x" />

Sinus

alt="" src="https://cdn.utakatikotak.com/finder/grafik-fungsi-sinus-baku.jpg" style="height:168px; width:464px" />

Cosinus

alt="" src="https://cdn.utakatikotak.com/finder/grafik-fungsi-cosinus-baku.jpg" style="height:168px; width:467px" />

Tangen

alt="" src="https://cdn.utakatikotak.com/finder/grafik-fungsi-tangen-baku.jpg" style="height:297px; width:467px" />

2. Grafik fungsi  alt="f(x) = a\sin x" src="https://s0.wp.com/latex.php?latex=f%28x%29+%3D+a%5Csin+x&bg=f9f9f9&fg=000000&s=0" title="f(x) = a\sin x" />;  alt="f(x) = a\cos x" src="https://s0.wp.com/latex.php?latex=f%28x%29+%3D+a%5Ccos+x&bg=f9f9f9&fg=000000&s=0" title="f(x) = a\cos x" />; dan  alt="f(x) = a\tan x" src="https://s0.wp.com/latex.php?latex=f%28x%29+%3D+a%5Ctan+x&bg=f9f9f9&fg=000000&s=0" title="f(x) = a\tan x" />

Didapat dari grafik trigonometri baku dengan cara mengalikan koordinat setiap titik pada grafik baku dengan bilangan a, sedangkan absisnya tetap. Periode grafik tetap  alt="2\pi" src="https://s0.wp.com/latex.php?latex=2%5Cpi&bg=f9f9f9&fg=000000&s=0" title="2\pi" /> untuk kosinus dan sinus. Sedangankan periode tangen  alt="\pi" src="https://s0.wp.com/latex.php?latex=%5Cpi&bg=f9f9f9&fg=000000&s=0" title="\pi" />.

Sinus

Misalkan  alt="a = 2" src="https://s0.wp.com/latex.php?latex=a+%3D+2&bg=f9f9f9&fg=000000&s=0" title="a = 2" />, maka grafiknya :

alt="" src="https://cdn.utakatikotak.com/finder/grafik-a-sin-x.jpg" style="height:240px; width:328px" />

Kosinus

Misalkan  alt="a = 2" src="https://s0.wp.com/latex.php?latex=a+%3D+2&bg=f9f9f9&fg=000000&s=0" title="a = 2" />, maka grafiknya

alt="" src="https://cdn.utakatikotak.com/finder/grafik-a-cos-x.jpg" style="height:240px; width:234px" />

Tangen

Misalkan alt="a = 2" src="https://s0.wp.com/latex.php?latex=a+%3D+2&bg=f9f9f9&fg=000000&s=0" title="a = 2" />, maka grafiknya

alt="" src="https://cdn.utakatikotak.com/finder/grafik-a-tan-x.jpg" style="height:311px; width:394px" />

3. Grafik fungsi  alt="f(x) = a\sin kx" src="https://s0.wp.com/latex.php?latex=f%28x%29+%3D+a%5Csin+kx&bg=f9f9f9&fg=000000&s=0" title="f(x) = a\sin kx" />;  alt="f(x) = a\cos kx" src="https://s0.wp.com/latex.php?latex=f%28x%29+%3D+a%5Ccos+kx&bg=f9f9f9&fg=000000&s=0" title="f(x) = a\cos kx" />; dan  alt="f(x) = a\tan kx" src="https://s0.wp.com/latex.php?latex=f%28x%29+%3D+a%5Ctan+kx&bg=f9f9f9&fg=000000&s=0" title="f(x) = a\tan kx" />

Didapat dari grafik trigonometri baku dengan cara mengalikan ordinat setiap titik pada grafik baku dengan bilangan a, sedangkan periode grafik sinus dan kosinus menjadi :

alt="\frac{2\pi}{\mid k\mid}" src="https://s0.wp.com/latex.php?latex=%5Cfrac%7B2%5Cpi%7D%7B%5Cmid+k%5Cmid%7D&bg=f9f9f9&fg=000000&s=0" title="\frac{2\pi}{\mid k\mid}" />

Dan tangen

alt="\frac{\pi}{\mid k\mid}" src="https://s0.wp.com/latex.php?latex=%5Cfrac%7B%5Cpi%7D%7B%5Cmid+k%5Cmid%7D&bg=f9f9f9&fg=000000&s=0" title="\frac{\pi}{\mid k\mid}" />

• Sinus

Misalkan  alt="a = 1" src="https://s0.wp.com/latex.php?latex=a+%3D+1&bg=f9f9f9&fg=000000&s=0" title="a = 1" /> dan  alt="k = 2" src="https://s0.wp.com/latex.php?latex=k+%3D+2&bg=f9f9f9&fg=000000&s=0" title="k = 2" />, maka grafiknya

alt="" src="https://cdn.utakatikotak.com/finder/a-sin-2x.jpg" style="height:240px; width:365px" />

• Kosinus

Misalkan  alt="a = 1" src="https://s0.wp.com/latex.php?latex=a+%3D+1&bg=f9f9f9&fg=000000&s=0" title="a = 1" />dan  alt="k = 2" src="https://s0.wp.com/latex.php?latex=k+%3D+2&bg=f9f9f9&fg=000000&s=0" title="k = 2" />, maka grafiknya

alt="" src="https://cdn.utakatikotak.com/finder/a-cos-2x.jpg" style="height:240px; width:358px" />

• Tangen

Misalkan a=1 alt="a = 1" src="https://s0.wp.com/latex.php?latex=a+%3D+1&bg=f9f9f9&fg=000000&s=0" title="a = 1" /> dan k=3 alt="k = 3" src="https://s0.wp.com/latex.php?latex=k+%3D+3&bg=f9f9f9&fg=000000&s=0" title="k = 3" />, maka grafiknya

alt="" src="https://cdn.utakatikotak.com/finder/a-tan-3x.jpg" style="height:240px; width:383px" />

1. Jika fungsi kosinus  alt="y = f(x) = a \cos (bx + c) + d" src="https://s0.wp.com/latex.php?latex=y+%3D+f%28x%29+%3D+a+%5Ccos+%28bx+%2B+c%29+%2B+d&bg=f9f9f9&fg=000000&s=0" title="y = f(x) = a \cos (bx + c) + d" />, maka nilai maksimumnya  alt="y_{maks} = \mid a\mid + d" src="https://s0.wp.com/latex.php?latex=y_%7Bmaks%7D+%3D+%5Cmid+a%5Cmid+%2B+d&bg=f9f9f9&fg=000000&s=0" title="y_{maks} = \mid a\mid + d" /> dan nilai minimumnya  alt="y_{min} = -\mid a\mid + d" src="https://s0.wp.com/latex.php?latex=y_%7Bmin%7D+%3D+-%5Cmid+a%5Cmid+%2B+d&bg=f9f9f9&fg=000000&s=0" title="y_{min} = -\mid a\mid + d" />

Jika  alt="y = f(x)" src="https://s0.wp.com/latex.php?latex=y+%3D+f%28x%29&bg=f9f9f9&fg=000000&s=0" title="y = f(x)" /> adalah fungsi periodik dengan nilai maksimum  alt="y_{maks}" src="https://s0.wp.com/latex.php?latex=y_%7Bmaks%7D&bg=f9f9f9&fg=000000&s=0" title="y_{maks}" /> dan minimum  alt="y_{min}" src="https://s0.wp.com/latex.php?latex=y_%7Bmin%7D&bg=f9f9f9&fg=000000&s=0" title="y_{min}" />, maka amplitudonya adalah :

Dengan demikian, fungsi sinus  alt="f(x) = \sin x" src="https://s0.wp.com/latex.php?latex=f%28x%29+%3D+%5Csin+x&bg=f9f9f9&fg=000000&s=0" title="f(x) = \sin x" />vatau  alt="f(x) = \sin x^{\circ}" src="https://s0.wp.com/latex.php?latex=f%28x%29+%3D+%5Csin+x%5E%7B%5Ccirc%7D&bg=f9f9f9&fg=000000&s=0" title="f(x) = \sin x^{\circ}" /> dan fungsi kosinus  alt="f(x) = cos x" src="https://s0.wp.com/latex.php?latex=f%28x%29+%3D+cos+x&bg=f9f9f9&fg=000000&s=0" title="f(x) = cos x" /> atau  alt="f(x) = cos x^{\circ}" src="https://s0.wp.com/latex.php?latex=f%28x%29+%3D+cos+x%5E%7B%5Ccirc%7D&bg=f9f9f9&fg=000000&s=0" title="f(x) = cos x^{\circ}" /> adalah fungsi periodik dengan periode dasar  alt="2\pi" src="https://s0.wp.com/latex.php?latex=2%5Cpi&bg=f9f9f9&fg=000000&s=0" title="2\pi" />atau  alt="360^{\circ}" src="https://s0.wp.com/latex.php?latex=360%5E%7B%5Ccirc%7D&bg=f9f9f9&fg=000000&s=0" title="360^{\circ}" />.