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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