Find the Exact Value sin(-810)

Problem

sin(−810^∘)

Solution

1. Identify the angle in degrees and find its coterminal equivalent within the standard range of 0^∘ to 360^∘

2. Add multiples of 360^∘ to the negative angle until it is positive.

−810^∘+360^∘=−450^∘

−450^∘+360^∘=−90^∘

−90^∘+360^∘=270^∘

3. Evaluate the sine function at the coterminal angle 270^∘

4. Recall the coordinates on the unit circle at 270^∘ which are (0,−1)

5. Determine the sine value, which corresponds to the ycoordinate.

sin(270^∘)=−1

Final Answer

sin(−810^∘)=−1

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