Find the Exact Value cos(7/3*pi)

Problem

cos((7*π)/3)

Solution

1. Identify the angle and determine if it is within the standard interval [0,2*π] Since (7*π)/3>2*π we need to find a coterminal angle.

2. Subtract 2*π from the angle to find the coterminal angle within the first rotation.

(7*π)/3−2*π=(7*π)/3−(6*π)/3

(7*π)/3−(6*π)/3=π/3

3. Evaluate the cosine of the coterminal angle π/3 using the unit circle or special right triangles.

cos(π/3)=1/2

Final Answer

cos((7*π)/3)=1/2

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