Question

The point (5,10) is on the terminal side of an angle θ in standard position. 

What is the value of 7 cotθ - 7 cos θ rounded to 3 decimal places?

Answer 1

In standard position, the angle is at the origin and the terminal side is inclined at an angle of θ, where:

tanθ=y/x=10/5=2; cotθ=½. The length along the incline up to the point (5,10) is √(5²+10²)=5√5. So cosθ=5/(5√5)=√5/5.

7cotθ-7cosθ=7(½-√5/5)=7(5-2√5)/10=0.36950 approx, 0.370 to 3 decimal places.