Find the Exact Value sin(510)

Problem

sin(510)

Solution

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

510−360=150

2. Determine the quadrant of the angle 150 Since 90<150<180 the angle lies in Quadrant II.

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

180−150=30

4. Determine the sign of the sine function in Quadrant II. Since sine is positive in the second quadrant, sin(150) will be positive.

sin(150)=sin(30)

5. Evaluate the sine of the reference angle using known trigonometric values.

sin(30)=1/2

Final Answer

sin(510)=1/2

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