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

Want more problems? Check here!