SOLUTION: Given tanx=8/15 and sin>0 what is the value of cosx

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Question 820348: Given tanx=8/15 and sin>0 what is the value of cosx
Found 2 solutions by jsmallt9, MathTherapy:
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
A drawing might help:
  1. Draw a right triangle.
  2. Choose one of the acute angles. Let's call it angle A.
  3. Label the sides so that tan(A) = 8/15. Since tan is opposite/adjacent, make the length of the side opposite angle A an 8 and make the length of the side adjacent to A a 15.
Since we're looking for cos and since cos is adjacent/hypotenuse, we will need to find the hypotenuse. Use the Pythagorean Theorem:
8%5E2+%2B+15%5E2+=+h%5E2 (where "h" represents the length of the hypotenuse)
64+%2B+225+=+h%5E2
289+=+h%5E2
Square root of each side. (Since h can only be positive, we will use just the positive square root.)
17+=+h

Since tan(A) is positive, since we were told that sin(A) > 0 (positive) and since tan is sin/cos, cos must be positive. So:
cos%28A%29+=+8%2F17

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

Given tan x = 8/15 and sin > 0 what is the value of cos x 


Since tan x = 8%2F15, and sin x > 0, then x is in the 1st quadrant, where all are positive (> 0)

tan x = o%2Fa+=+y%2Fx+=+8%2F15, and so: y = 8; and x = 15 

r+=+sqrt%28y%5E2+%2B+x%5E2%29______r+=+sqrt%288%5E2+%2B+15%5E2%29______r+=+sqrt%2864+%2B+225%29_______r+=+sqrt%28289%29_______r = 17  

cos x = a%2Fh+=+x%2Fr+=+highlight_green%2815%2F17%29

You can do the check!! 



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