Find the Exact Value csc(-630)

Problem

csc(−630)

Solution

1. Find a coterminal angle by adding 360 to the given angle until it falls within the standard range of 0 to 360

−630+360=−270

−270+360=90

2. Apply the reciprocal identity for the cosecant function, which states that csc(θ)=1/sin(θ)

csc(−630)=csc(90)

csc(90)=1/sin(90)

3. Evaluate the sine function at 90 using the unit circle, where the ycoordinate at 90 is 1

sin(90)=1

4. Simplify the expression by substituting the value of the sine function back into the reciprocal identity.

1/1=1

Final Answer

csc(−630)=1

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