Evaluate sin(420 degrees )

Problem

sin(420)

Solution

1. Identify the angle as being greater than 360 which means it completes more than one full rotation 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.

420−360=60

3. Apply the property that trigonometric functions of coterminal angles are equal.

sin(420)=sin(60)

4. Evaluate the sine of the reference angle using the known values for special angles.

sin(60)=√(,3)/2

Final Answer

sin(420)=√(,3)/2

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