Evaluate sin(390 degrees )

Problem

sin(390^∘)

Solution

1. Identify the angle as being greater than 360^∘ which means it has completed 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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