Find the Exact Value cos((25pi)/6)

Problem

cos((25*π)/6)

Solution

1. Identify the angle and determine if it is greater than one full rotation (2*π.

2. Find the coterminal angle by subtracting multiples of 2*π until the angle is within the interval [0,2*π)

(25*π)/6=(24*π+π)/6

(25*π)/6=4*π+π/6

3. Simplify the expression using the periodicity of the cosine function, cos(θ+2*k*π)=cos(θ)

cos((25*π)/6)=cos(π/6+2*(2*π))

cos((25*π)/6)=cos(π/6)

4. Evaluate the cosine of the reference angle π/6 (or 30 using the unit circle or special right triangles.

cos(π/6)=√(,3)/2

Final Answer

cos((25*π)/6)=√(,3)/2

Want more problems? Check here!