precal question

Question

Consider the following.

t = 13π/6

(a) Find the reference number t for the value of t.

t = 

 

(b) Find the terminal point determined by t.

(x, y) =

 

 

Answer 1

(a) θ = 13π /6 = 2π + π/6 is in the first quadrant and is co-terminal with π/6. So the reference angle is π/6.

(b) To find the terminal point we also need the radial distance or radius. If we assume that we are interested in the terminal point in a unit circle, then P(x,y) = (cos θ, sin θ) = (cos 13π /6, sin 13π /6) = (cos π/6, sin π/6) = ((√3)/2, 1/2). If the radial distance is r then P(x,y) = (rcos θ, rsin θ) = ((√3)r/2, r/2).