Find the Exact Value cos(arctan(11/60))

Problem

cos(arctan(11/60))

Solution

1. Identify the inner expression as an angle θ=arctan(11/60) which implies tan(θ)=11/60

2. Relate the tangent function to the sides of a right triangle where tan(θ)=opposite/adjacent

3. Assign the opposite side length as 11 and the adjacent side length as 60

4. Calculate the hypotenuse h using the Pythagorean theorem a2+b2=h2

60+11=h2

3600+121=h2

3721=h2

h=√(,3721)=61

5. Determine the value of cos(θ) using the ratio adjacent/hypotenuse

cos(θ)=60/61

Final Answer

cos(arctan(11/60))=60/61

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