sinθ = 1/2 and cosθ = -√3/2, what is the value of θ?

Assessment: WAEC SSCE - General Mathematics - 1989 (Objective) Subject: General Mathematics

Question 1 Report

sinθ = 1/2 and cosθ = -√3/2, what is the value of θ?
Answer Details
We can use the fact that sin2θ + cos2θ = 1, to find the value of sinθ or cosθ given the other one. Since sinθ = 1/2, we know that sin2θ + cos2θ = 1 becomes: (1/2)2 + cos2θ = 1 Simplifying the equation, we get: 1/4 + cos2θ = 1 cos2θ = 3/4 Taking the square root of both sides, we get: cosθ = ±√3/2 Since we know that cosθ = -√3/2, we can conclude that θ = 150o (or 5π/6 radians) as this is the angle in the fourth quadrant that has a cosine of -√3/2. Therefore, the answer is option E: 150o.
Read lesson note on Logarithms (WAEC)
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