Find the Exact Value csc(-450)

Problem

csc(−450^∘)

Solution

1. Use the property of odd functions to move the negative sign outside the function, since csc(−θ)=−csc(θ)

csc(−450^∘)=−csc(450^∘)

2. Find the coterminal angle by subtracting 360^∘ from 450^∘ to bring the angle within the standard 0^∘ to 360^∘ range.

450^∘−360^∘=90^∘

3. Rewrite the expression using the coterminal angle.

−csc(450^∘)=−csc(90^∘)

4. Apply the reciprocal identity csc(θ)=1/sin(θ)

−csc(90^∘)=−1/sin(90^∘)

5. Substitute the known value sin(90^∘)=1 into the expression.

−1/1=−1

Final Answer

csc(−450^∘)=−1

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