Find the values of the six trigonometric functions

Question

The terminal side of  lies on the given line in the specified quadrant. Find the values of the six trigonometric functions of by finding a point on the line.

y = - x

lies in Quadrant II.

Answer 1

Step 1:

Definitions of trigonometric functions of any angle:

Let be an angle in standard position with a point on the terminal side of and then

      

Step 2:    

The equation of line is .

In second quadrant and .

Consider , then

The point on the line is .

Thus, the obtained values are , and

Step 3:

Step 4:

Step 5:

Step 6:

Step 7:

Step 8:

 

Solution:

The six trigonometric function values: