F. 2 Garfik Fungsi Trigonometri
F. 2. 1 Grafik Fungsi Sinus
$\color{blue}\begin{array}{|c|c|c|c|c|c|c|c|c|c| }\hline \color{magenta}x&0&\frac{\pi }{6}&\frac{\pi }{4}&\frac{\pi }{3}&\frac{\pi }{2}&\frac{2\pi }{3}&\frac{3\pi }{4}&\frac{5\pi }{6}&\pi \\\hline \color{red}f(x)&0&\frac{1}{2}&\frac{1}{2}\sqrt{2}&\frac{1}{2}\sqrt{3}&1&\frac{1}{2}\sqrt{3}&\frac{1}{2}\sqrt{2}&\frac{1}{2}&0\\\hline \color{magenta}x&\frac{7\pi }{6}&\frac{5\pi }{4}&\frac{4\pi }{3}&\frac{3\pi }{2}&\frac{5\pi }{3}&\frac{7\pi }{4}&\frac{11\pi }{6}&2\pi & \\\hline \color{red}f(x)&-\frac{1}{2}&-\frac{1}{2}\sqrt{2}&-\frac{1}{2}\sqrt{3}&-1&-\frac{1}{2}\sqrt{3}&-\frac{1}{2}\sqrt{2}&-\frac{1}{2}&0&\\\hline \end{array}$.
F. 2. 2 Grafik Fungsi Cosinus
$\color{blue}\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}\hline \color{black}x&0&\frac{\pi }{6}&\frac{\pi }{4}&\frac{\pi }{3}&\frac{\pi }{2}&\frac{2\pi }{3}&\frac{3\pi }{4}&\frac{5\pi }{6}&\pi \\\hline \color{red}f(x)&1&\frac{1}{2}\sqrt{3}&\frac{1}{2}\sqrt{2}&\frac{1}{2}&0&-\frac{1}{2}&-\frac{1}{2}\sqrt{2}&-\frac{1}{2}\sqrt{3}&-1\\\hline \color{black}x&\frac{7\pi }{6}&\frac{5\pi }{4}&\frac{4\pi }{3}&\frac{3\pi }{2}&\frac{5\pi }{3}&\frac{7\pi }{4}&\frac{11\pi }{6}&2\pi&\\\hline \color{red}f(x)&-\frac{1}{2}\sqrt{3}&-\frac{1}{2}\sqrt{2}&-\frac{1}{2}&0&\frac{1}{2}&\frac{1}{2}\sqrt{2}&\frac{1}{2}\sqrt{3}&1&\\\hline \end{array}$.
F. 2. 3 Grafik Fungsi Tangen
$\color{blue}\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}\hline \color{black}x&0&\frac{\pi }{6}&\frac{\pi }{4}&\frac{\pi }{3}&\frac{\pi }{2}&\frac{2\pi }{3}&\frac{3\pi }{4}&\frac{5\pi }{6}&\pi \\\hline \color{red}f(x)&0&\frac{1}{3}\sqrt{3}&1&\sqrt{3}&\infty &-\sqrt{3}&-1&-\frac{1}{3}\sqrt{3}&0\\\hline \color{black}x&\frac{7\pi }{6}&\frac{5\pi }{4}&\frac{4\pi }{3}&\frac{3\pi }{2}&\frac{5\pi }{3}&\frac{7\pi }{4}&\frac{11\pi }{6}&2\pi&\\\hline \color{red}f(x)&\frac{1}{3}\sqrt{3}&1&\sqrt{3}&\infty &-\sqrt{3}&-1&-\frac{1}{3}\sqrt{3}&0&\\\hline \end{array}$.
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
$\begin{aligned}&\textrm{untuk bentuk}\\ &f(x)=\begin{cases} y &=a\sin bx+c \\ y &=a\cos bx+c \\ y & =a\tan bx+c \end{cases}\\ &\begin{array}{|c|l|l|}\hline 1.&a&\textrm{Amplitudo}\\\hline 2.&b&\textrm{Periode}\\\hline 3.&c&\textrm{Geseran}\\\hline \end{array} \end{aligned}$.
$\LARGE\colorbox{yellow}{ CONTOH SOAL}$.
$\begin{array}{ll}\\ 1.&\textrm{Gambarlah grafik fungsi berikut} \\ &\textrm{jika}\: \: 0^{\circ}\leq x\leq 360^{\circ}\\ &\textrm{a}.\quad f(x)=-2\sin x\\ &\textrm{b}.\quad f(x)=3\cos x\\ &\textrm{c}.\quad f(x)=\displaystyle \frac{1}{2}\sin x\\ &\textrm{d}.\quad f(x)=4\cos x\\ &\textrm{e}.\quad f(x)=2\tan x\\\\&\color{blue}\textrm{Jawab}:\\&\begin{aligned}& \end{aligned} \end{array}$.
$.\: \qquad\begin{aligned}&\color{blue}\textrm{No.1 a}\\ &y=f(x)=-2\sin x=a\sin bx+c\\ &\begin{array}{|c|l|l|l|}\hline 1.&a&\textrm{Amplitudo}&\left |-2 \right |=2\\\hline 2.&b&\textrm{Periode}&\displaystyle \frac{2\pi }{b}=2\pi \Leftrightarrow b=1\\\hline 3.&c&\textrm{Geseran}&0\\\hline \end{array} \end{aligned}$.$.\: \qquad\begin{aligned}&\color{blue}\textrm{No.1 b}\\ &y=f(x)=3\cos x=a\cos bx+c\\ &\begin{array}{|c|l|l|l|}\hline 1.&a&\textrm{Amplitudo}&\left |3 \right |=3\\\hline 2.&b&\textrm{Periode}&\displaystyle \frac{2\pi }{b}=2\pi \Leftrightarrow b=1\\\hline 3.&c&\textrm{Geseran}&0\\\hline \end{array} \end{aligned}$.
$.\: \qquad\begin{aligned}&\color{blue}\textrm{No.1 c}\\ &y=f(x)=\displaystyle \frac{1}{2}\sin x=a\sin bx+c\\ &\begin{array}{|c|l|l|l|}\hline 1.&a&\textrm{Amplitudo}&\left |\displaystyle \frac{1}{2} \right |=\displaystyle \frac{1}{2}\\\hline 2.&b&\textrm{Periode}&\displaystyle \frac{2\pi }{b}=2\pi \Leftrightarrow b=1\\\hline 3.&c&\textrm{Geseran}&0\\\hline \end{array} \end{aligned}$.
$.\: \qquad\begin{aligned}&\color{blue}\textrm{No.1 d}\\ &y=f(x)=\displaystyle 4\cos x=a\cos bx+c\\ &\begin{array}{|c|l|l|l|}\hline 1.&a&\textrm{Amplitudo}&\left |\displaystyle 4 \right |=\displaystyle 4\\\hline 2.&b&\textrm{Periode}&\displaystyle \frac{2\pi }{b}=2\pi \Leftrightarrow b=1\\\hline 3.&c&\textrm{Geseran}&0\\\hline \end{array} \end{aligned}$.
$.\: \qquad\begin{aligned}&\color{blue}\textrm{No.1 e}\\ &y=f(x)=\displaystyle 2\tan x=a\tan bx+c\\ &\begin{array}{|c|l|l|l|}\hline 1.&a&\textrm{Amplitudo}&\left |\displaystyle 2 \right |=\displaystyle 2\\\hline 2.&b&\textrm{Periode}&\displaystyle \frac{2\pi }{b}=2\pi \Leftrightarrow b=1\\\hline 3.&c&\textrm{Geseran}&0\\\hline \end{array} \end{aligned}$.
$\begin{array}{ll}\\ 2.&\textrm{Gambarlah grafik fungsi berikut} \\ &\textrm{jika}\: \: 0^{\circ}\leq x\leq 360^{\circ}\\ &\textrm{a}.\quad f(x)=\left |-2\sin x \right |\\ &\textrm{b}.\quad f(x)=\left |3\cos x \right |\\ &\textrm{c}.\quad f(x)=\left |\displaystyle \frac{1}{2}\sin x \right |\\ &\textrm{d}.\quad f(x)=\left |4\cos x \right |\\ &\textrm{e}.\quad f(x)=\left |2\tan x \right |\\\\&\color{blue}\textrm{Jawab}:\\&\begin{aligned}& \end{aligned} \end{array}$.
$.\: \qquad\begin{aligned}&\color{blue}\textrm{No.2 a}\\ &y=f(x)=\left |-\displaystyle 2\sin x \right |=\left |a\sin bx+c \right |\\ &\begin{array}{|c|l|l|l|}\hline 1.&a&\textrm{Amplitudo}&\left |\displaystyle 2 \right |=\displaystyle 2\\\hline 2.&b&\textrm{Periode}&\pi \Leftrightarrow b=1\\\hline 3.&c&\textrm{Geseran}&0\\\hline \end{array} \end{aligned}$.
$.\: \qquad\begin{aligned}&\color{blue}\textrm{No.2 b}\\ &y=f(x)=\left |\displaystyle 3\cos x \right |=\left |a\cos bx+c \right |\\ &\begin{array}{|c|l|l|l|}\hline 1.&a&\textrm{Amplitudo}&\left |\displaystyle 3 \right |=\displaystyle 3\\\hline 2.&b&\textrm{Periode}&\pi \Leftrightarrow b=1\\\hline 3.&c&\textrm{Geseran}&0\\\hline \end{array} \end{aligned}$.
$\LARGE\colorbox{yellow}{LATIHAN SOAL}$.
Silahkan selesaikan soal yg belum dibahas
DAFTAR PUSTAKA
- Yuana, R.A., Indriyastuti. 2017. Perspektif Matematika untuk Kelas X SMA dan MA Kelompok Mata Pelajaran Wajib. Solo: TIGA SERANGKAI PUSTAKA MANDIRI.
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