Find the Exact Value csc(30 degrees )

Problem

csc(30^∘)

Solution

1. Identify the definition of the cosecant function in terms of the sine function.

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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