Find the Exact Value sin(390)

Problem

sin(390)

Solution

1. Identify the angle as being greater than 360 which means it completes more than one full revolution around the unit circle.

2. Find the coterminal angle by subtracting 360 from the given angle to find an equivalent angle within the standard 0 to 360 range.

390−360=30

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

sin(390)=sin(30)

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

sin(30)=1/2

Final Answer

sin(390)=1/2

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