Find the Exact Value csc(-225 degrees )

Problem

csc(−225)

Solution

1. Use the odd function property of the cosecant function, which states csc(−θ)=−csc(θ)

csc(−225)=−csc(225)

2. Find the reference angle for 225 Since 225 is in the third quadrant, the reference angle is 225−180=45

Reference Angle=45

3. Determine the sign of the cosecant function in the third quadrant. Since sin(θ) is negative in the third quadrant, csc(θ) is also negative.

csc(225)=−csc(45)

4. Substitute this back into the expression from step 1.

−csc(225)=−(−csc(45))

csc(−225)=csc(45)

5. Evaluate the cosecant of the reference angle. Since sin(45)=√(,2)/2 its reciprocal is √(,2)

csc(45)=√(,2)

Final Answer

csc(−225)=√(,2)

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