SOLUTION: I have to solve the composition and state whether it is an angle or ratio: cos(tan^-1(5/12)) I came up with .923 and that it is a ratio. Is this right?

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Question 813588: I have to solve the composition and state whether it is an angle or ratio:
cos(tan^-1(5/12))
I came up with .923 and that it is a ratio.
Is this right?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
tan%5E%28-1%29%285%2F12%29 represents an angle. Specifically it represents an angle whose tan is 5/12. Your expression is, in effect, the cos of the angle whose tan is 5/12. To find the answer:
  1. Draw a right triangle.
  2. Choose one of the acute angles. This will be the tan%5E%28-1%29%285%2F12%29 angle.
  3. Label the sides of the triangle so that the tan is 5/12. Since tan is opposite over adjacent, label the opposite side as 5 and the adjacent side as 12.
  4. Since cos is adjacent over hypotenuse, we will need the hypotenuse. Use the Pythagorean Theorem to find the hypotenuse. (You should get 13.)
  5. So cos%28tan%5E%28-1%29%285%2F12%29%29 is 12/13. This is an exact answer.

I assume you used a calculator to get 0.923. This is a rounded-off approximation of 12/13. 12/13 is a better answer.