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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