SOLUTION: Find the values of the six trigonometric functions for the angle in standard position determined by the points (-3,4). Thanks.

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Question 1015529: Find the values of the six trigonometric functions for the angle in standard position determined by the points (-3,4).
Thanks.

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
In the figure below we calculate the hypotenuse by the
Pythagorean theorem using ADJACENT as the x-coordinate
of (-3,4), which is -3, and using OPPOSITE as the y-coordinate
of (-3,4), which is 4:

HYPOTENUSE%5E2%22%22=%22%22ADJACENT%5E2%2BOPPOSITE%5E2
HYPOTENUSE%5E2%22%22=%22%22%28-3%29%5E2%2B%28%22%22%2B4%29%5E2
HYPOTENUSE%5E2%22%22=%22%229%2B16
HYPOTENUSE%5E2%22%22=%22%2225
HYPOTENUSE%22%22=%22%22sqrt%2825%29
HYPOTENUSE%22%22=%22%225





Then we use the definition of the 6 trig ratios, being sure
to watch the signs + and -

sin%28theta%29%22%22=%22%22OPPOSITE%2FHYPOTENUSE%22%22=%22%22%28%22%22%2B4%29%2F%28%22%22%2B5%29%22%22=%22%224%2F5

cos%28theta%29%22%22=%22%22ADJACENT%2FHYPOTENUSE%22%22=%22%22%28%22%22-3%29%2F%28%22%22%2B5%29%22%22=%22%22-3%2F5

tan%28theta%29%22%22=%22%22OPPOSITE%2FADJACENT%22%22=%22%22%28%22%22%2B4%29%2F%28%22%22-3%29%22%22=%22%22-4%2F3

sec%28theta%29%22%22=%22%22HYPOTENUSE%2FADJACENT%22%22=%22%22%28%22%22%2B5%29%2F%28%22%22-3%29%22%22=%22%22-5%2F3

csc%28theta%29%22%22=%22%22HYPOTENUSE%2FOPPOSITE%22%22=%22%22%28%22%22%2B5%29%2F%28%22%22%2B4%29%22%22=%22%225%2F4

cot%28theta%29%22%22=%22%22ADJACENT%2FOPPOSITE%22%22=%22%22%28%22%22-3%29%2F%28%22%22%2B4%29%22%22=%22%22-3%2F4

Edwin