SOLUTION: Find the value of the following expression: sec(tan^-1(5/12))

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Question 1138380: Find the value of the following expression: sec(tan^-1(5/12))
Found 2 solutions by KMST, ikleyn:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Thereis an infinite number of sets of three integers that can be the length of the sides of a right triangle.
Such sets of integers are called Pythagorean triples, and you can find lists of them by searching online for "Pythagorean triples".
Teachers like to use them in problems.
{3,4,5} is the most popular (and easiest to remember),
but 5%2C12%2C13 is also a popular one.
Here is a right triangle with such shape:
tan%28B%29=5%2F12 , so tan%5E%22-1%22%285%2F12%29=B , and cos%28B%29=5%2F13 ,
so sec%28B%29%22=%221%2Fcos%28B%29%22=%22%285%2F12%29%5E%22-1%22%22=%22highlight%2812%2F5=2.4%29

Answer by ikleyn(52909) About Me  (Show Source):
You can put this solution on YOUR website!
.
They want you find  sec(x)  given that  tan(x) = 5%2F12.


It means that the opposite leg  "a"  is 5, while the adjacent leg  "b"  is 12.


Then the hypotenuse is  c = sqrt%28a%5E2+%2B+b%5E2%29 = sqrt%285%5E2+%2B+12%5E2%29 = sqrt%2825+%2B+144%29 = sqrt%28169%29 = 13


and  cos(x) = b%2Fc = 12%2F13.


Hence,  sec(x) = 1%2Fcos%28x%29 = 1%2F%28%2812%2F13%29%29 = 13%2F12.    ANSWER

Solved.

It is your standard "mantra" in solving such problems.


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Do not accept any different answer,  since it  is / (or would be)  incorrect.


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Dear tutor @KMST, I am glad to see you returned back to this forum after long absence !