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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