Find the Exact Value tan((7pi)/2)

Problem

tan((7*π)/2)

Solution

1. Identify the angle in terms of its position on the unit circle.

2. Simplify the angle by subtracting multiples of 2*π to find the coterminal angle within the interval [0,2*π)

(7*π)/2−2*π=(7*π)/2−(4*π)/2

(3*π)/2

3. Apply the definition of the tangent function in terms of sine and cosine.

tan((3*π)/2)=sin((3*π)/2)/cos((3*π)/2)

4. Evaluate the sine and cosine at the angle (3*π)/2

sin((3*π)/2)=−1

cos((3*π)/2)=0

5. Determine the value by substituting the coordinates into the tangent ratio.

tan((3*π)/2)=(−1)/0

6. Conclude that since division by zero is undefined, the tangent of the angle does not exist.

Final Answer

tan((7*π)/2)=undefined

Want more problems? Check here!