Can Someone Help Please.

Question

Find the reference angle associated with each rotation and then find the associated point (x,y) on the unit circle. a) 13pi/4 b) 13pi/6 c)-13pi/3 d)7pi/2

Answer 1

A reference angle is an acute angle on the terminal side of the quadrants.

 

 

a)

 

13π/4

 

13π/4 = (12π + π) / 4

          = 3π + (π/4)

 

 

The reference angle is π/4.  So if we went 3π radians in a unit circle from this reference angle, we would be in the 3rd quadrant.  Since π/4 is a symmetrical angle in any quadrant, the coordinate of this angle is

 

(-√(2)/2 , -√(2)/2).

 

 

Note: The general coordinates are     (cos(reference angle), sin(reference angle))

 

 

b)

 

13π/6 = (12π + π) / 6

         = 2π + (π/6)

 

 

The reference angle is π/6.  If we went 2π in a unit circle from the reference angle, we would end up in the 1st quadrant.  The coordinate of the reference angle is

 

(√(3)/2 , 1/2).

 

 

Can you try the last two problems on your own using the approach I showed you?