Evaluate 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 into the identity.

csc(30^∘)=1/sin(30^∘)

3. Recall the value of the sine of 30^∘ from the unit circle or a standard 30−60−90 triangle.

sin(30^∘)=1/2

4. Simplify the expression by dividing 1 by the fraction.

csc(30^∘)=1/(1/2)

csc(30^∘)=2

Final Answer

csc(30^∘)=2

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