Find the Exact Value cos(-7pi)

Problem

cos(−7*π)

Solution

1. Use the parity property of the cosine function, which is an even function, meaning cos(−θ)=cos(θ)

cos(−7*π)=cos(7*π)

2. Apply periodicity to find the coterminal angle within the interval [0,2*π) Since the period of cosine is 2*π subtract multiples of 2*π from the argument.

7*π−3*(2*π)=π

3. Simplify the expression using the coterminal angle found in the previous step.

cos(7*π)=cos(π)

4. Evaluate the cosine at π using the unit circle, where the coordinates at π radians are (−1,0)

cos(π)=−1

Final Answer

cos(−7*π)=−1

Want more problems? Check here!