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

Want more problems? Check here!