Find the Exact Value csc(210 degrees )

Problem

csc(210^∘)

Solution

1. Identify the reference angle by determining how far 210^∘ is from the horizontal axis.

210^∘−180^∘=30^∘

2. Determine the quadrant of the angle. Since 210^∘ is between 180^∘ and 270^∘ it lies in Quadrant III.

3. Recall the sign of the cosecant function in Quadrant III. In this quadrant, both sine and cosecant are negative.

csc(210^∘)=−csc(30^∘)

4. Apply the reciprocal identity for cosecant.

csc(30^∘)=1/sin(30^∘)

5. Substitute the known value sin(30^∘)=1/2 into the expression.

csc(30^∘)=1/(1/2)=2

6. Combine the value with the correct sign from step 3.

csc(210^∘)=−2

Final Answer

csc(210^∘)=−2

Want more problems? Check here!