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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