Find the Exact Value csc(30)

Problem

csc(30)

Solution

1. Identify the relationship between the cosecant function and the sine function using the reciprocal identity.

csc(θ)=1/sin(θ)

2. Substitute the given angle of 30 into the identity.

csc(30)=1/sin(30)

3. Recall the exact value of sin(30) from the unit circle or a special right triangle (30−60−90.

sin(30)=1/2

4. Calculate the reciprocal of the sine value to find the cosecant.

csc(30)=1/(1/2)

5. Simplify the fraction by multiplying by the reciprocal of the denominator.

csc(30)=2

Final Answer

csc(30)=2

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