Question

Determine the exact values of the six trigonometric functions of the angle .

Answer 1

(a) The point  is 

Step 1:

The above coordinate pair in first quadrant.

Angle is in first quadrant.

Graph:

.

From Pythagorean theorem,

.

Step 2:

Six trigonometric functions are

, , ,

, , .

Substitute the values of  in above ratios

, , ,

, , .

Solution:

Six trigonometric functions are , , , , and .

Answer 2

b) The point  is 

Step 1:

The above coordinate pair in second quadrant.

Angle is in second quadrant.

Graph:

From Pythagorean theorem,

.

Step 2:

Six trigonometric functions are

, , ,

, , .

Substitute the values of  in above ratios

, , ,

, , .

Solution:

Six trigonometric functions are  , , ,

, and .