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

Problem

cos((25*π)/2)

Solution

1. Identify the angle and its periodicity. The cosine function has a period of 2*π

2. Simplify the fraction by dividing the numerator by the denominator.

(25*π)/2=12.5*π

3. Subtract multiples of 2*π to find the coterminal angle within the range [0,2*π)

12.5*π−6*(2*π)=12.5*π−12*π

(25*π)/2−6*π=π/2

4. Evaluate the cosine of the coterminal angle.

cos(π/2)=0

Final Answer

cos((25*π)/2)=0

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