P1^
7
Solving(^) equations
(^) using
(^) graphs
(^) of
(^) trigonometrical
(^) functions
231
ExAmPlE 7.5 Find values of θ in the interval −360° θ 360° for which sin θ = 0.5.
SOlUTION
sin θ = 0.5 ⇒ sin–1 0.5 = 30° ⇒ θ = 30°. Figure 7.20 shows the graph of sin θ.
The values of θ for which sin θ = 0.5 are −330°, −210°, 30°, 150°.
ExAmPlE 7.6 Solve the equation 3tan θ = −1 for −180° θ 180°.
SOlUTION
3tan θ = − 1
⇒ tan θ = −^13
⇒ θ = tan–1 (^) (−^13 )
⇒ θ = −18.4° to 1 d.p. (calculator).
From figure 7.21, the other answer in the range is
θ = −18.4° + 180°
= 161.6°
The values of θ are −18.4° or 161.6° to 1 d.p.
–1
–330° –210° O 30° 150° θ
1
0.5
sin θ
Figure 7.20
θ
y = 3tan θ
–18.4°
y
–270° –180° –90° O 13 90° 270°
161.6°
- 180°
Figure 7.21