# Bab 16 Fungsi Trigonometri

5.7.4 Fungsi Trigonometri, SPM Praktis (Kertas 1)

Soalan 9:
Given that $\mathrm{sin}\theta =\frac{3}{5}$, dengan keadaan θ ialah sudut tirus, tanpa menggunakan jadual atau kalkulator, cari nilai bagi
(a)    sin (180º + θ),
(b)   kos (180º – θ),
(c)    tan (360º + θ).

Peneyelesaian:
(a)
sin (180º + θ)
= sin 180º kos θ + kos 180º sin θ
= (0) kos θ + (– 1) sin θ
= – sin θ
$=-\frac{3}{5}$

(b)
kos (180º – θ)
= kos 180º kos θ + sin 180º sin θ
= (– 1) kos θ + (0) sin θ
= – kos θ
$=-\frac{4}{5}$

(c)
$\begin{array}{l}\mathrm{tan}\left({360}^{\circ }+\theta \right)\\ \\ =\frac{\mathrm{tan}{360}^{\circ }+\mathrm{tan}\theta }{1-\mathrm{tan}{360}^{\circ }\mathrm{tan}\theta }\\ \\ =\frac{0+\mathrm{tan}\theta }{1-\left(0\right)\left(\mathrm{tan}\theta \right)}\\ =\mathrm{tan}\theta \\ =\frac{3}{4}\end{array}$

Soalan 10:
Buktikan setiap identiti trigonometri yang berikut.
(a) kot2 x – kot2 x kos2x = kos2 x

Peneyelesaian:
(a)
Sebelah kiri:
kot2 x– kot2 x kos2 x
= kot2 x (1 – kos2 x)
= kot2 x (sin2 x)

(b)