Grafik Fungsi Trigonometri

Sebelumnya telah diketahui perbandingan trigonometri diberbagai kuadan dan sudut-sudut yang berelasi, selanjutnya dapat digambarkan garfik fungsinya, yaitu : $y=\sin x$, $y=\cos x$, dan $y=\tan x$.

A. Grafik Fungsi Sinus

Berikut ilustrasi grafik fungsi sinus untuk  $-\pi \le x\le \pi$.

$\begin{array}{rl}& \mathbf{\text{Bentuk umum}}\\ & f(x)=a\sin b(x+c)+d\\ & \bullet \text{periode}:{\displaystyle \frac{{360}^{\circ }}{b}\text{atau}{\displaystyle \frac{2\pi }{\left|b\right|}}}\\ & \bullet \text{nilai maksimum}:\left|a\right|\\ & \bullet \text{nilai minimum}:-\left|a\right|\\ & \bullet \text{geseran grafik ke kiri}:c\\ & \bullet \text{geseran grafik ke kanan}:-c\\ & \bullet \text{geseran grafik ke atas}:d\\ & \bullet \text{geseran grafik ke bawah}:-d\end{array}$.

B. Grafik Fungsi Cosinus

Berikut ilustrasi grafik fungsi sinus untuk  $-\pi \le x\le \pi$.

$\begin{array}{rl}& \mathbf{\text{Bentuk umum}}\\ & f(x)=a\cos b(x+c)+d\\ & \bullet \text{periode}:{\displaystyle \frac{{360}^{\circ }}{b}\text{atau}{\displaystyle \frac{2\pi }{\left|b\right|}}}\\ & \bullet \text{nilai maksimum}:\left|a\right|\\ & \bullet \text{nilai minimum}:-\left|a\right|\\ & \bullet \text{geseran grafik ke kiri}:c\\ & \bullet \text{geseran grafik ke kanan}:-c\\ & \bullet \text{geseran grafik ke atas}:d\\ & \bullet \text{geseran grafik ke bawah}:-d\end{array}$.

C. Grafik Fungsi Tangen

Berikut ilustrasi grafik fungsi sinus untuk  $-\pi \le x\le \pi$.

$\begin{array}{rl}& \mathbf{\text{Bentuk umum}}\\ & f(x)=a\tan b(x+c)+d\\ & \bullet \text{periode}:{\displaystyle \frac{{180}^{\circ }}{b}\text{atau}{\displaystyle \frac{\pi }{\left|b\right|}}}\\ & \bullet \text{nilai maksimum}:\mathit{\text{tidak ada}}\\ & \bullet \text{nilai minimum}:\mathit{\text{tidak ada}}\\ & \bullet \text{geseran grafik ke kiri}:c\\ & \bullet \text{geseran grafik ke kanan}:-c\\ & \bullet \text{geseran grafik ke atas}:d\\ & \bullet \text{geseran grafik ke bawah}:-d\end{array}$.

$\text{CONTOH SOAL}$.

$\begin{array}{l}\\ 1.& \text{Diketahui fungsi}f(x)={\displaystyle \frac{4}{5}\sin (2x-{\displaystyle \frac{\pi }{3}})}\\ & \text{tentukanlah}\\ & \text{a}.\text{periode}\\ & \text{b}.\text{nilai maksimu}\\ & \text{c}.\text{nilai minimum}\\ & \text{d}.\text{arah geseran fungsinya}\\ & \text{e}.\text{gambarlah grafik fungsinya}\\ \\ & \mathbf{\text{Jawab}}:\\ & \begin{array}{rl}\text{Diket}& \text{ahui bahwa}\\ f(x)& ={\displaystyle \frac{4}{5}\sin (2x-{\displaystyle \frac{\pi }{3}})}\\ & ={\displaystyle \frac{4}{5}\sin 2(x-{\displaystyle \frac{\pi }{6}})\text{atau boleh juga}}\\ & \text{dituliskan dengan bentuk}\\ & ={\displaystyle \frac{4}{5}\sin 2(x-{30}^{\circ })}\end{array}\\ & \begin{array}{rl}\text{a}.& \text{Periodenya}:\left|{\displaystyle \frac{{360}^{\circ }}{2}}\right|={180}^{\circ }\\ \text{b}.& \text{Nilai maksimumnya}:\left|{\displaystyle \frac{4}{5}}\right|=\frac{4}{5}\\ \text{c}.& \text{Nilai minimumnya}:-\left|{\displaystyle \frac{4}{5}}\right|=-\frac{4}{5}\\ \text{d}.& \text{Arah geserannya ke kanan sejauh}:{30}^{\circ }\\ \text{e}.& \text{Berikut gambar ilustrasinya}\end{array}\end{array}$.

$\begin{array}{l}\\ 2.& \text{Diketahui fungsi}f(x)=2\cos (2x-{\displaystyle \frac{\pi }{4}})\\ & \text{tentukanlah}\\ & \text{a}.\text{periode}\\ & \text{b}.\text{nilai maksimu}\\ & \text{c}.\text{nilai minimum}\\ & \text{d}.\text{arah geseran fungsinya}\\ & \text{e}.\text{gambarlah grafik fungsinya}\\ \\ & \mathbf{\text{Jawab}}:\\ & \begin{array}{rl}\text{Diket}& \text{ahui bahwa}\\ f(x)& =2\cos (2x-{\displaystyle \frac{\pi }{4}})\\ & =2\cos 2(x-{\displaystyle \frac{\pi }{8}})\text{atau boleh juga}\\ & \text{dituliskan dengan bentuk}\\ & =2\cos 2(x-22,5^{\circ })\end{array}\\ & \begin{array}{rl}\text{a}.& \text{Periodenya}:\left|{\displaystyle \frac{{360}^{\circ }}{2}}\right|={180}^{\circ }\\ \text{b}.& \text{Nilai maksimumnya}:\left|2\right|=2\\ \text{c}.& \text{Nilai minimumnya}:-\left|2\right|=-2\\ \text{d}.& \text{Arah geserannya ke kanan sejauh}:22,5^{\circ }\\ \text{e}.& \text{Berikut gambar ilustrasinya}\end{array}\end{array}$.

$\begin{array}{l}\\ 3.& \text{Diketahui fungsi}f(x)=\tan (2x-{\displaystyle \frac{\pi }{4}})\\ & \text{tentukanlah}\\ & \text{a}.\text{periode}\\ & \text{b}.\text{nilai maksimu}\\ & \text{c}.\text{nilai minimum}\\ & \text{d}.\text{arah geseran fungsinya}\\ & \text{e}.\text{gambarlah grafik fungsinya}\\ \\ & \mathbf{\text{Jawab}}:\\ & \begin{array}{rl}\text{Diket}& \text{ahui bahwa}\\ f(x)& =\tan (2x-{\displaystyle \frac{\pi }{4}})\\ & =\tan 2(x-{\displaystyle \frac{\pi }{8}})\text{atau boleh juga}\\ & \text{dituliskan dengan bentuk}\\ & =\tan 2(x-22,5^{\circ })\end{array}\\ & \begin{array}{rl}\text{a}.& \text{Periodenya}:\left|{\displaystyle \frac{{180}^{\circ }}{2}}\right|={90}^{\circ }\\ \text{b}.& \text{Nilai maksimumnya}:\mathit{\text{tidak ada}}\\ \text{c}.& \text{Nilai minimumnya}:\mathit{\text{tidak ada}}\\ \text{d}.& \text{Arah geserannya ke kanan sejauh}:22,5^{\circ }\\ \text{e}.& \text{Berikut gambar ilustrasinya}\end{array}\end{array}$.