SOLUTION: 6) find csc(arctan 8/15) a) 17/8 b) 8/17 c) 15/17 d) 17/15 e) Undefined

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Question 121955: 6) find csc(arctan 8/15)
a) 17/8
b) 8/17
c) 15/17
d) 17/15
e) Undefined
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First a triangle with legs of 8 and 15. Let x be the angle we'll refer to.




By using pythagorean's theorem, we find that the hypotenuse is 17 units





Since tan%28x%29=opposite%2Fadjacent this means x=arctan%288%2F15%29 (notice how the arctangent is gives you an angle)

Now remember sin%28x%29=opposite%2Fhypotenuse and csc%28x%29=hypotenuse%2Fopposite (remember the cosecant and sine function are reciprocals of each other)

So csc%28x%29=17%2F8


which also means

csc%28arctan%288%2F15%29%29=17%2F8

So the answer is A)