Evaluate -csc(pi/4)^2

Problem

−csc(π/4)

Solution

1. Identify the trigonometric value for sin(π/4)

sin(π/4)=√(,2)/2

2. Determine the cosecant value by taking the reciprocal of the sine value.

csc(π/4)=1/sin(π/4)

csc(π/4)=2/√(,2)

csc(π/4)=√(,2)

3. Square the cosecant value as indicated by the exponent.

(√(,2))2=2

4. Apply the negative sign to the squared result.

−(2)=−2

Final Answer

−csc(π/4)=−2

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