Find the Exact Value cos(-pi/2)

Problem

cos(−π/2)

Solution

1. Identify the angle in the unit circle. The angle is −π/2 radians, which corresponds to a 90^∘ rotation in the clockwise direction from the positive x-axis.

2. Determine the coordinates of the point on the unit circle at this angle. Rotating −π/2 radians from (1,0) lands on the point (0,−1)

3. Apply the definition of the cosine function on the unit circle. For any point (x,y) on the unit circle, cos(θ)=x

4. Extract the x-coordinate from the point (0,−1)

Final Answer

cos(−π/2)=0

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