Question

P (-7,-2) is a point on the terminal side of θ in standard position. Find the exact value of the six trigonometric functions for θ.

Answer 1

The answer to your question is below

Explanation:

Data

Point = (-7 , -2)

six trigonometric functions

Process

1.- Plot the point, See the graph below

2.- This point is in the third quadrant.

3.- The coordinates of the points gives the adjacent side (-7) and the opposite side (-2).

4.- The the hypotenuse

h² = (-7)² + (-2)²

h² = 49 + 4

h² = 53

h =
`√(53)`

5.- Find the trigonometric functions

sin Ф = -2/
`√(53)`

cos Ф = -7/
`√(53)`

tan Ф = -2/-7 = 2/7

cot Ф = 7/2

sec Ф =
`- √(53) / 7`

csc Ф =
`- √(53) / 2`