If 2 sin x° - 1 = 0 and x° is an acute angle; find:

(i) sin x°

(ii) x°

(iii) cos x° and

(iv) tan x°.

(i) 2 sin x° - 1 = 0

⇒ 2 sin x° = 1

⇒ sin x° = $\dfrac{1}{2}$

Hence, sin x° = $\dfrac{1}{2}$.

(ii) x°

⇒ sin x° = $\dfrac{1}{2}$

⇒ sin x° = sin 30°

Hence, x° = 30°.

(iii) cos x°

⇒ cos 30° = $\dfrac{\sqrt3}{2}$

Hence, cos x° = $\dfrac{\sqrt3}{2}$.

(iv) tan x°.

⇒ tan 30° = $\dfrac{1}{\sqrt3}$

Hence, tan x° = $\dfrac{1}{\sqrt3}$.