Help please homework

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

The first thing we can do with this angle is simplify it. 13π/6 = (12π + π)/6 = (12π/6) + (π/6) = 2π + (π/6). 2π is a full circle in radian form, just like 360 degrees is a full circle in degree form. After going 2π radians around, we end up back at the starting point. Then we go another π/6 around, so our angle ends up being π/6. To find our terminal point, we need to look at the unit circle, which is a circle surrounding the origin of a graph with the radius of 1 unit. We start from the rightmost point, which has an x-value of 1 and a y-value of 0, then go counterclockwise around the circle by the value of our angle. So now, we're at the terminal point (√3/2, 1/2). We still need to find the reference number, and that is the y-value of our terminal point.

a) 1/2

b) (√3/2, 1/2)