If sin 3y = cos 2y and 0o \(\leq\) 90o, find the value of y
Answer Details
Using the identity sin(90° - θ) = cos θ, we can write cos 2y as sin (90° - 2y), and so sin 3y = sin (90° - 2y).
Since the sine function is periodic with a period of 360°, we can write:
3y = 90° - 2y + 360°k or 3y = 270° - 2y + 360°k for some integer k.
Solving for y in each equation gives:
5y = 90° + 360°k or 5y = 270° + 360°k
Dividing both sides by 5 gives:
y = 18° + 72°k or y = 54° + 72°k
Since the problem specifies that 0° ≤ y ≤ 90°, the only solution that works is y = 18°. Therefore, the answer is (a) 18°.