Find the Exact Value cos((-19pi)/2)

Problem

cos(−(19*π)/2)

Solution

1. Use the even-odd property of the cosine function, which states that cos(−θ)=cos(θ)

cos(−(19*π)/2)=cos((19*π)/2)

2. Find a coterminal angle by dividing the numerator by the denominator to identify the number of full rotations.

19/2=9.5

3. Subtract multiples of 2*π (which is (4*π)/2 to find an angle within the interval [0,2*π)

(19*π)/2−4*π=(11*π)/2

(11*π)/2−4*π=(3*π)/2

4. Identify the coordinates on the unit circle for the angle (3*π)/2 The point is (0,−1)

cos((3*π)/2)=0

Final Answer

cos(−(19*π)/2)=0

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