Find the Exact Value sin(-225 degrees )

Problem

sin(−225)

Solution

1. Find the coterminal angle by adding 360 to the negative angle to locate it within the standard 0 to 360 range.

θ=−225+360=135

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

3. Determine the sign of the sine function in Quadrant II. In this quadrant, sin(θ) is positive.

4. Calculate the reference angle θ′ using the formula for Quadrant II.

θ′=180−135=45

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

sin(45)=√(,2)/2

Final Answer

sin(−225)=√(,2)/2

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