document.write( "Question 615576: if sin theta=4/5 and theta terminates on the interval [0, pi/2] find the exact value of tan 2theta \n" ); document.write( "

Algebra.Com's Answer #387268 by jsmallt9(3758) $\"\"$ $\"About$

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For $\"tan%282theta%29\"$ we have the formula:
\n" ); document.write( " $\"tan%282theta%29+=+2tan%28theta%29%2F%281-tan%5E2%28theta%29%29\"$
For the formula we need $\"tan%28theta%29\"$
For $\"tan%28theta%29\"$ we need the opposite side, the adjacent side and the quadrant that $\"theta\"$ terminates in. We're given the quadrant.
Since $\"sin%28theta%29+=+4%2F5\"$ and since sin is opposite over hypotenuse, we can use 4 for the opposite side and 5 for the hypotenuse.
We can use the 4 and the 5 and the Pythagorean Theorem to find the adjacent side. (Be sure to put the 4, the 5 and your variable in the correct places in the equation. Hint: The hypotenuse is always the longest side in a right triangle.)
Form $\"tan%28theta%29\"$ by putting the opposite side, 4, over the adjacent side you just figured out. (And since $\"theta\"$ terminates in the 1st quadrant, we will use the positive ration of opposite over adjacent).)
Take the $\"tan%28theta%29\"$ you just got and put it in the two spots for $\"tan%28theta%29\"$ in
\n" ); document.write( " $\"tan%282theta%29+=+2tan%28theta%29%2F%281-tan%5E2%28theta%29%29\"$
\n" ); document.write( "and simplify.

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