Find the Exact Value csc(-90)

Problem

csc(−90)

Solution

1. Identify the trigonometric identity for the cosecant function, which is the reciprocal of the sine function.

csc(θ)=1/sin(θ)

2. Substitute the given angle into the identity.

csc(−90)=1/sin(−90)

3. Apply the odd function property of sine, which states that sin(−θ)=−sin(θ)

sin(−90)=−sin(90)

4. Evaluate the sine of 90 using the unit circle.

sin(90)=1

5. Calculate the final value by substituting the result back into the reciprocal expression.

csc(−90)=1/(−1)

Final Answer

csc(−90)=−1

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