Find the Exact Value csc(450)

Problem

csc(450)

Solution

1. Identify the angle and its periodicity. Since the cosecant function has a period of 360 we can find a coterminal angle by subtracting 360 from 450

θ=450−360

θ=90

2. Apply the reciprocal identity for cosecant. The cosecant of an angle is the reciprocal of the sine of that same angle.

csc(90)=1/sin(90)

3. Evaluate the sine of the coterminal angle. On the unit circle, the sine of 90 corresponds to the y-coordinate at the top of the circle.

sin(90)=1

4. Substitute the value back into the reciprocal expression to find the final result.

csc(90)=1/1

csc(90)=1

Final Answer

csc(450)=1

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