document.write( "Question 820348: Given tanx=8/15 and sin>0 what is the value of cosx \n" ); document.write( "

Algebra.Com's Answer #493488 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
A drawing might help:

Draw a right triangle.
Choose one of the acute angles. Let's call it angle A.
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:
\n" ); document.write( " $\"8%5E2+%2B+15%5E2+=+h%5E2\"$ (where \"h\" represents the length of the hypotenuse)
\n" ); document.write( " $\"64+%2B+225+=+h%5E2\"$
\n" ); document.write( " $\"289+=+h%5E2\"$
\n" ); document.write( "Square root of each side. (Since h can only be positive, we will use just the positive square root.)
\n" ); document.write( " $\"17+=+h\"$

\n" ); document.write( "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:
\n" ); document.write( " $\"cos%28A%29+=+8%2F17\"$ \n" ); document.write( "

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