Find the Exact Value sin((11pi)/2)

Problem

sin((11*π)/2)

Solution

1. Identify the angle (11*π)/2 and determine its position on the unit circle by finding a coterminal angle within the interval [0,2*π)

2. Divide the coefficient 11 by the denominator 2 to express the fraction as a mixed number.

(11*π)/2=5.5*π

3. Subtract multiples of 2*π to find the coterminal angle.

5.5*π−4*π=1.5*π

(11*π)/2−2*(2*π)=(3*π)/2

4. Evaluate the sine function at the coterminal angle (3*π)/2 On the unit circle, the point corresponding to (3*π)/2 is (0,−1)

sin((3*π)/2)=−1

Final Answer

sin((11*π)/2)=−1

Want more problems? Check here!