Find the Exact Value csc(300)

Problem

csc(300)

Solution

1. Identify the reference angle by finding the difference between the given angle and the nearest multiple of 180 Since 300 is in the fourth quadrant, the reference angle is 360−300=60

2. Determine the sign of the cosecant function in the fourth quadrant. In the fourth quadrant, sine and its reciprocal, cosecant, are negative.

3. Apply the reciprocal identity for cosecant, which states that csc(θ)=1/sin(θ)

4. Evaluate the sine of the reference angle. We know that sin(60)=√(,3)/2

5. Calculate the cosecant by taking the negative reciprocal of the sine value.

csc(300)=−1/sin(60)

csc(300)=−2/√(,3)

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

csc(300)=−(2√(,3))/3

Final Answer

csc(300)=−(2√(,3))/3

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