Find the Exact Value csc(-300 degrees )

Problem

csc(−300)

Solution

1. Find the coterminal angle by adding 360 to the negative angle to find its equivalent position within the first rotation.

−300+360=60

2. Identify the trigonometric identity for cosecant, which is the reciprocal of the sine function.

csc(−300)=csc(60)

csc(60)=1/sin(60)

3. Determine the sine value for 60 using the unit circle or special right triangles.

sin(60)=√(,3)/2

4. Calculate the reciprocal to find the value of the cosecant function.

csc(60)=1/√(,3)/2

csc(60)=2/√(,3)

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

2/√(,3)⋅√(,3)/√(,3)=(2√(,3))/3

Final Answer

csc(−300)=(2√(,3))/3

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