do know how to work this

Question

Suppose that the terminal point determined by t is the point

5

13

, 

12

13

on the unit circle. Find the terminal point determined by each of the following.

(a)    

π − t

(x, y) = 

(b)    

−t

(x, y) = 

(c)    

π + t

(x, y) = 

(d)    

2π + t

(x, y) = 

 

Answer 1

Step 1:

The terminal point is .

Observe the terminal point.

Here and , hence lies in Quadrant I.

(a)

Find the terminal point determined by .

Since lies in Quadrant I, lies in Quadrant II.

is a angle in Quadrant II, hence .

The terminal point is .

Step 2:

(b)

Find the terminal point determined by .

is reflection along -axis.

Since lies in Quadrant I, lies in Quadrant IV.

is a angle in Quadrant IV, hence .

The terminal point is .

Step 3:

(c)

Find the terminal point determined by .

Since lies in Quadrant I, lies in Quadrant III.

is a angle in Quadrant III, hence .

The terminal point is .

Step 4:

(d)

Find the terminal point determined by .

Since lies in Quadrant I, lies in Quadrant I.

is a angle in Quadrant I, hence .

The terminal point is .

Solution:

(a) The terminal point is .

(b) The terminal point is .

(c) The terminal point is .

(d) The terminal point is .