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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