Simplify csc(150)

Problem

csc(150)

Solution

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

csc(150)=1/sin(150)

2. Determine the reference angle for 150 by subtracting it from 180 since it is in the second quadrant.

(θ_ref)=180−150=30

3. Evaluate the sine of the angle, noting that sine is positive in the second quadrant.

sin(150)=sin(30)

4. Substitute the known value of sin(30)=1/2 into the expression.

sin(150)=1/2

5. Calculate the reciprocal to find the final value of the cosecant function.

csc(150)=1/(1/2)=2

Final Answer

csc(150)=2

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