Find the Exact Value sin(495)

Problem

sin(495)

Solution

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

495−360=135

2. Identify the quadrant for 135 Since 90<135<180 the angle lies in Quadrant II.

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

180−135=45

4. Apply the sine sign rule for Quadrant II. The sine function is positive in the second quadrant.

sin(135)=sin(45)

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

sin(45)=√(,2)/2

Final Answer

sin(495)=√(,2)/2

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