If sin 3y = cos 2y and 0o \(\leq\) 90o, find the value of y

Assessment: WAEC SSCE - General Mathematics - 2010 (Objective) Subject: General Mathematics

Question 1 Report

If sin 3y = cos 2y and 0^o \(\leq\) 90^o, find the value of y

18^o

36^o

54^o

90^o

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°.

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Sine, Cosine And Tangent Of An Angle

Trigonometry

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If sin 3y = cos 2y and 0o \(\leq\) 90o, find the value of y

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