Find the Exact Value cos(-900)

Problem

cos(−900^∘)

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.

−900^∘+360^∘=−540^∘

−540^∘+360^∘=−180^∘

−180^∘+360^∘=180^∘

3. Determine the cosine of the coterminal angle 180^∘ using the unit circle.

4. Recall that at 180^∘ the coordinates on the unit circle are (−1,0) where the x-coordinate represents the cosine value.

cos(180^∘)=−1

Final Answer

cos(−900^∘)=−1

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