Find the Exact Value sin(480)

Problem

sin(480)

Solution

1. Find the coterminal angle by subtracting 360 from the given angle to bring it within the standard range of 0 to 360

480−360=120

2. Identify the quadrant for 120 Since 90<120<180 the angle lies in Quadrant II.

3. Determine the reference angle for an angle in Quadrant II by subtracting the angle from 180

180−120=60

4. Apply the sign rule for the sine function. In Quadrant II, the sine of an angle is positive.

sin(120)=sin(60)

5. Evaluate the exact value using the known trigonometric values for special angles.

sin(60)=√(,3)/2

Final Answer

sin(480)=√(,3)/2

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