Find the Exact Value csc((25pi)/2)

Problem

csc((25*π)/2)

Solution

1. Identify the period of the cosecant function, which is 2*π

2. Simplify the angle by finding its coterminal equivalent within the interval [0,2*π) by subtracting multiples of 2*π

3. Calculate the number of full rotations: (25*π)/2=12.5*π

4. Subtract 12*π (which is 6×2*π from the angle: (25*π)/2−(24*π)/2=π/2

5. Apply the definition of cosecant as the reciprocal of the sine function: csc(π/2)=1/sin(π/2)

6. Evaluate the sine of π/2 which is 1

7. Divide to find the final value: 1/1=1

Final Answer

csc((25*π)/2)=1

Want more problems? Check here!