Find the Exact Value csc(-600)

Problem

csc(−600)

Solution

1. Find the coterminal angle by adding multiples of 360 to the negative angle until it falls within the range [0,360)

−600+2*(360)=−600+720=120

2. Identify the trigonometric identity for cosecant in terms of sine.

csc(120)=1/sin(120)

3. Determine the reference angle for 120 which is in the second quadrant.

(θ_ref)=180−120=60

4. Evaluate the sine of the angle. Since 120 is in the second quadrant, the sine value is positive.

sin(120)=sin(60)=√(,3)/2

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

csc(120)=1/√(,3)/2=2/√(,3)

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

2/√(,3)⋅√(,3)/√(,3)=(2√(,3))/3

Final Answer

csc(−600)=(2√(,3))/3

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