Find the Exact Value (cos(-7pi))/2

Problem

cos(−7*π)/2

Solution

1. Identify the angle within the cosine function. The angle is −7*π

2. Apply the property of periodicity for the cosine function. Since cos(θ+2*π*k)=cos(θ) for any integer k we can add 8*π (which is 4×2*π to the angle to find a coterminal angle.

3. Calculate the coterminal angle: −7*π+8*π=π

4. Evaluate the cosine of the coterminal angle. We know that cos(π)=−1

5. Substitute this value back into the original expression and divide by the denominator.

Final Answer

cos(−7*π)/2=−1/2

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