Find the Exact Value csc(300 degrees )

Problem

csc(300)

Solution

1. Identify the reference angle for 300 Since 300 is in the fourth quadrant, the reference angle is calculated as 360−300=60

2. Determine the sign of the cosecant function in the fourth quadrant. In the fourth quadrant, the sine function is negative, and since csc(θ)=1/sin(θ) the cosecant function is also negative.

3. Apply the reference angle property.

csc(300)=−csc(60)

4. Evaluate the cosecant of the reference angle. We know that sin(60)=√(,3)/2 so its reciprocal is:

csc(60)=2/√(,3)

5. Rationalize the denominator by multiplying the numerator and denominator by √(,3)

2/√(,3)⋅√(,3)/√(,3)=(2√(,3))/3

6. Combine the value with the negative sign determined in step 2.

csc(300)=−(2√(,3))/3

Final Answer

csc(300)=−(2√(,3))/3

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