# Bab 16 Fungsi Trigonometri

5.7.3 Fungsi Trigonometri, SPM Praktis (Kertas 1)

Soalan 7:
Diberi bahawa , dengan keadaan A ialah sudut cakah dan B ialah sudut tirus. Cari
(a)    tan A
(b)   sin (A + B)
(c)    kos (A B)

Peneyelesaian:

(a)
$\mathrm{tan}A=-\frac{5}{12}$

(b)
$\begin{array}{l}\mathrm{sin}\left(A+B\right)=\mathrm{sin}AkosB+kosA\mathrm{sin}B\\ \mathrm{sin}\left(A+B\right)\\ =\left(\frac{5}{13}\right)\left(\frac{4}{5}\right)+\left(-\frac{12}{13}\right)\left(\frac{3}{5}\right)←\overline{)\begin{array}{l}kosA=-\frac{12}{13}\\ \mathrm{sin}B=\frac{3}{5}\end{array}}\\ =\frac{4}{13}-\frac{36}{65}\\ =-\frac{16}{65}\end{array}$

(c)
$\begin{array}{l}kos\left(A-B\right)=kosAkosB+\mathrm{sin}A\mathrm{sin}B\\ kos\left(A-B\right)=\left(-\frac{12}{13}\right)\left(\frac{4}{5}\right)+\left(\frac{5}{13}\right)\left(\frac{3}{5}\right)\\ kos\left(A-B\right)=-\frac{33}{65}\end{array}$

Soalan 8:
Jika sin A = p, dan 90° < A < 180 °, ungkap dalam sebutan p
(a)    tan A
(b)   cos A
(c)    sin 2A

Peneyelesaian:

(a)

(b)

(c)
$\begin{array}{l}\mathrm{sin}A=2\mathrm{sin}AkosA\\ \mathrm{sin}A=2\left(p\right)\left(-\sqrt{1-{p}^{2}}\right)\\ \mathrm{sin}A=-2p\sqrt{1-{p}^{2}}\end{array}$