SOLUTION: the pt (5,12) is on the terminal side of an angle that is in standard position. find the value of the six trigonometric function

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Question 626404: the pt (5,12) is on the terminal side of an angle that is in standard position. find the value of the six trigonometric function
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
The point (5, 12) is in the first quadrant. So all the functions will have positive values. All we have to do is find the ratios. The 5 will be the adjacent side and the 12 will be the opposite side. We just have to find the hypotenuse and we'll be ready to go.

To find the hypotenuse we use the Pythagorean Theorem:
5%5E2+%2B+12%5E2+=+x%5E2
25+%2B+144+=+x%5E2
169+=+x%5E2
13+=+x
Lets call the angle in question angle A.
sin(A) = opposite/hypotenuse = 12/13
cos(A) = adjacent/hypotenuse = 5/13
tan(A) = opposite/adjacent = 12/5
csc(A) = 1/sin(A) = 13/12
sec(A) = 1/cos(A) = 13/5
cot(A) = 1/tan(A) = 5/12