Lanjutan Materi Fungsi Trigonometri dan Grafiknya

F. 2 Garfik Fungsi Trigonometri

F. 2. 1 Grafik Fungsi Sinus

$\begin{array}{|cccccccccc|}\hline x& 0& \frac{\pi }{6}& \frac{\pi }{4}& \frac{\pi }{3}& \frac{\pi }{2}& \frac{2\pi }{3}& \frac{3\pi }{4}& \frac{5\pi }{6}& \pi \\ f(x)& 0& \frac{1}{2}& \frac{1}{2}\sqrt{2}& \frac{1}{2}\sqrt{3}& 1& \frac{1}{2}\sqrt{3}& \frac{1}{2}\sqrt{2}& \frac{1}{2}& 0\\ x& \frac{7\pi }{6}& \frac{5\pi }{4}& \frac{4\pi }{3}& \frac{3\pi }{2}& \frac{5\pi }{3}& \frac{7\pi }{4}& \frac{11\pi }{6}& 2\pi & \\ f(x)& -\frac{1}{2}& -\frac{1}{2}\sqrt{2}& -\frac{1}{2}\sqrt{3}& -1& -\frac{1}{2}\sqrt{3}& -\frac{1}{2}\sqrt{2}& -\frac{1}{2}& 0& \\ \hline\end{array}$.

F. 2. 2 Grafik Fungsi Cosinus

$\begin{array}{|cccccccccc|}\hline x& 0& \frac{\pi }{6}& \frac{\pi }{4}& \frac{\pi }{3}& \frac{\pi }{2}& \frac{2\pi }{3}& \frac{3\pi }{4}& \frac{5\pi }{6}& \pi \\ f(x)& 1& \frac{1}{2}\sqrt{3}& \frac{1}{2}\sqrt{2}& \frac{1}{2}& 0& -\frac{1}{2}& -\frac{1}{2}\sqrt{2}& -\frac{1}{2}\sqrt{3}& -1\\ x& \frac{7\pi }{6}& \frac{5\pi }{4}& \frac{4\pi }{3}& \frac{3\pi }{2}& \frac{5\pi }{3}& \frac{7\pi }{4}& \frac{11\pi }{6}& 2\pi & \\ f(x)& -\frac{1}{2}\sqrt{3}& -\frac{1}{2}\sqrt{2}& -\frac{1}{2}& 0& \frac{1}{2}& \frac{1}{2}\sqrt{2}& \frac{1}{2}\sqrt{3}& 1& \\ \hline\end{array}$.

F. 2. 3 Grafik Fungsi Tangen

$\begin{array}{|cccccccccc|}\hline x& 0& \frac{\pi }{6}& \frac{\pi }{4}& \frac{\pi }{3}& \frac{\pi }{2}& \frac{2\pi }{3}& \frac{3\pi }{4}& \frac{5\pi }{6}& \pi \\ f(x)& 0& \frac{1}{3}\sqrt{3}& 1& \sqrt{3}& \mathrm{\infty }& -\sqrt{3}& -1& -\frac{1}{3}\sqrt{3}& 0\\ x& \frac{7\pi }{6}& \frac{5\pi }{4}& \frac{4\pi }{3}& \frac{3\pi }{2}& \frac{5\pi }{3}& \frac{7\pi }{4}& \frac{11\pi }{6}& 2\pi & \\ f(x)& \frac{1}{3}\sqrt{3}& 1& \sqrt{3}& \mathrm{\infty }& -\sqrt{3}& -1& -\frac{1}{3}\sqrt{3}& 0& \\ \hline\end{array}$.

Pada fungsi Tangen demikian juga nanti Cotangennya ada beberapa nilai fungsinya yang tidak terdefinisi. Dalam fungsi Tangen fungsi, nilai fungsi yang tidak terdefini terdapat pada saat nilai  $x={\displaystyle \frac{\pi }{2}={90}^{\circ }}$ dan $x={\displaystyle \frac{3\pi }{2}={270}^{\circ }}$. Sehingga pada saat posisi nilai itu, maka dibuatlah garis bantu berupa garis putus-putus pada grafik yang dan ditampakkan berupa garis vertikal yang selanjutnya garis vertikal itu disebut sebagai asimtot.

F. 2. 4 Menggambar Grafik Fungsi Trigonometri

$\begin{array}{rl}& \text{untuk bentuk}\\ & f(x)=\{\begin{array}{ll}y& =a\sin bx+c\\ y& =a\cos bx+c\\ y& =a\tan bx+c\end{array}\\ & \begin{array}{|cll|}\hline 1.& a& \text{Amplitudo}\\ 2.& b& \text{Periode}\\ 3.& c& \text{Geseran}\\ \hline\end{array}\end{array}$.

$\text{ CONTOH SOAL}$.

$\begin{array}{l}\\ 1.& \text{Gambarlah grafik fungsi berikut}\\ & \text{jika}{0}^{\circ }\le x\le {360}^{\circ }\\ & \text{a}.f(x)=-2\sin x\\ & \text{b}.f(x)=3\cos x\\ & \text{c}.f(x)={\displaystyle \frac{1}{2}\sin x}\\ & \text{d}.f(x)=4\cos x\\ & \text{e}.f(x)=2\tan x\\ \\ & \text{Jawab}:\\ & \begin{array}{rl}& \end{array}\end{array}$.

$.\begin{array}{rl}& \text{No.1 a}\\ & y=f(x)=-2\sin x=a\sin bx+c\\ & \begin{array}{|clll|}\hline 1.& a& \text{Amplitudo}& |-2|=2\\ 2.& b& \text{Periode}& {\displaystyle \frac{2\pi }{b}=2\pi \iff b=1}\\ 3.& c& \text{Geseran}& 0\\ \hline\end{array}\end{array}$.

$.\begin{array}{rl}& \text{No.1 b}\\ & y=f(x)=3\cos x=a\cos bx+c\\ & \begin{array}{|clll|}\hline 1.& a& \text{Amplitudo}& \left|3\right|=3\\ 2.& b& \text{Periode}& {\displaystyle \frac{2\pi }{b}=2\pi \iff b=1}\\ 3.& c& \text{Geseran}& 0\\ \hline\end{array}\end{array}$.

$.\begin{array}{rl}& \text{No.1 c}\\ & y=f(x)={\displaystyle \frac{1}{2}\sin x=a\sin bx+c}\\ & \begin{array}{|clll|}\hline 1.& a& \text{Amplitudo}& \left|{\displaystyle \frac{1}{2}}\right|={\displaystyle \frac{1}{2}}\\ 2.& b& \text{Periode}& {\displaystyle \frac{2\pi }{b}=2\pi \iff b=1}\\ 3.& c& \text{Geseran}& 0\\ \hline\end{array}\end{array}$.

$.\begin{array}{rl}& \text{No.1 d}\\ & y=f(x)={\displaystyle 4\cos x=a\cos bx+c}\\ & \begin{array}{|clll|}\hline 1.& a& \text{Amplitudo}& \left|{\displaystyle 4}\right|={\displaystyle 4}\\ 2.& b& \text{Periode}& {\displaystyle \frac{2\pi }{b}=2\pi \iff b=1}\\ 3.& c& \text{Geseran}& 0\\ \hline\end{array}\end{array}$.

$.\begin{array}{rl}& \text{No.1 e}\\ & y=f(x)={\displaystyle 2\tan x=a\tan bx+c}\\ & \begin{array}{|clll|}\hline 1.& a& \text{Amplitudo}& \left|{\displaystyle 2}\right|={\displaystyle 2}\\ 2.& b& \text{Periode}& {\displaystyle \frac{2\pi }{b}=2\pi \iff b=1}\\ 3.& c& \text{Geseran}& 0\\ \hline\end{array}\end{array}$.

$\begin{array}{l}\\ 2.& \text{Gambarlah grafik fungsi berikut}\\ & \text{jika}{0}^{\circ }\le x\le {360}^{\circ }\\ & \text{a}.f(x)=|-2\sin x|\\ & \text{b}.f(x)=|3\cos x|\\ & \text{c}.f(x)=\left|{\displaystyle \frac{1}{2}\sin x}\right|\\ & \text{d}.f(x)=|4\cos x|\\ & \text{e}.f(x)=|2\tan x|\\ \\ & \text{Jawab}:\\ & \begin{array}{rl}& \end{array}\end{array}$.

$.\begin{array}{rl}& \text{No.2 a}\\ & y=f(x)=|-{\displaystyle 2\sin x}|=|a\sin bx+c|\\ & \begin{array}{|clll|}\hline 1.& a& \text{Amplitudo}& \left|{\displaystyle 2}\right|={\displaystyle 2}\\ 2.& b& \text{Periode}& \pi \iff b=1\\ 3.& c& \text{Geseran}& 0\\ \hline\end{array}\end{array}$.

$.\begin{array}{rl}& \text{No.2 b}\\ & y=f(x)=\left|{\displaystyle 3\cos x}\right|=|a\cos bx+c|\\ & \begin{array}{|clll|}\hline 1.& a& \text{Amplitudo}& \left|{\displaystyle 3}\right|={\displaystyle 3}\\ 2.& b& \text{Periode}& \pi \iff b=1\\ 3.& c& \text{Geseran}& 0\\ \hline\end{array}\end{array}$.

$\text{LATIHAN SOAL}$.

Silahkan selesaikan soal yg belum dibahas

DAFTAR PUSTAKA

1. Yuana, R.A., Indriyastuti. 2017. Perspektif Matematika untuk Kelas X SMA dan MA Kelompok Mata Pelajaran Wajib. Solo: TIGA SERANGKAI PUSTAKA MANDIRI.