need help with this

Question

Consider the following.

t = − 

23π

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

Step 1:

(a)

The value of is .

Find the reference number .

The reference number associated with is the shortest distance along the unit circle between the terminal points determined by and -axis.

Reference number is

Step 2:

(b)

Find the terminal number.

The point  obtained by moving along the unit circle in either clockwise or anti clockwise direction is the terminal distance.

The reference number is , the terminal point is .

Since lies in first quadrant, both .

Terminal point is .

Solution:

(a) Reference number is .

(b) Terminal point is .