Find the Exact Value csc(-270)

Problem

csc(−270^∘)

Solution

1. Identify the reference angle and the coterminal angle for −270^∘ by adding 360^∘

−270^∘+360^∘=90^∘

2. Apply the definition of the cosecant function, which is the reciprocal of the sine function.

csc(−270^∘)=csc(90^∘)

csc(90^∘)=1/sin(90^∘)

3. Evaluate the sine of 90^∘ using the unit circle, where the ycoordinate at 90^∘ is 1

sin(90^∘)=1

4. Substitute the value back into the cosecant expression.

1/1=1

Final Answer

csc(−270^∘)=1

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