1 Find all six trigonometric functions of if the given point

1. Find all six trigonometric functions of if the given point is on the terminal side of . (If an answer is undefined, enter UNDEFINED.)

(1, - sqrt 3)

2. Find all six trigonometric functions of if the given point is on the terminal side of . (Assume that a is a positive number. If an answer is undefined, enter UNDEFINED.)

(12a, 5a)

3. In the following diagram, angle is in standard position. In each case, find sin , cos , and tan .

4. Draw the following angle in standard position.

0°

Find a point on the terminal side.

(x, y) =

Find the sine, cosine, and tangent of the angle.

=

5. Indicate the two quadrants could terminate in given the value of the trigonometric function.

sin = 12/13

6. Indicate the two quadrants could terminate in given the value of the trigonometric function.

tan = 3/4

7. Find the remaining trigonometric functions of based on the given information.

cos = 12/37 and terminates in QII

Solution

1. Find all six trigonometric functions of if the given point is on the terminal side of .

(1, - sqrt 3) ; is in IVRT quadrant

hypotenuse = sqrt (1 +sqrt3)^2 ) = 2

sin = -sqrt3/2; cos = 1/2; tan = -sqrt3

sec = 2; csc = -2/sqrt3 ; cot = -1/sqrt3

2. Find all six trigonometric functions of if the given point is on the terminal side of . (Assume that a is a positive number. If an answer is undefined, enter UNDEFINED.)

(12a, 5a)

is in IIIrd quadrnat

hypotenuse = sqrt( (12a)^2 + (5a)^2) = 13a

sin = -5a/13a = - 5/13 ; csc = -13/5

cos = -12a/13a = -12/13 ; secv = -13/12

tan = -5a/-12a = 5/12 ; cot = 12/5

3) Hypotenuse = sqrt( 4^2 + 3^2) = 5

sin = 3/5 ; cos = 4/5 ;tan = 3/4