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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