Find the Exact Value sin(420)

Problem

sin(420)

Solution

1. Identify the angle as being greater than 360 and find its coterminal angle within the range [0,360) by subtracting 360

θ=420−360

θ=60

2. Apply the property of periodic functions, which states that sin(θ+360⋅n)=sin(θ)

sin(420)=sin(60)

3. Evaluate the sine of the reference angle using the unit circle or special right triangles.

sin(60)=√(,3)/2

Final Answer

sin(420)=√(,3)/2

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