SOLUTION: if sin theta=4/5 and theta terminates on the interval [0, pi/2] find the exact value of tan 2theta

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Question 615576: if sin theta=4/5 and theta terminates on the interval [0, pi/2] find the exact value of tan 2theta
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
  1. For tan%282theta%29 we have the formula:
    tan%282theta%29+=+2tan%28theta%29%2F%281-tan%5E2%28theta%29%29
  2. For the formula we need tan%28theta%29
  3. For tan%28theta%29 we need the opposite side, the adjacent side and the quadrant that theta terminates in. We're given the quadrant.
  4. 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.
  5. 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.)
  6. 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).)
  7. Take the tan%28theta%29 you just got and put it in the two spots for tan%28theta%29 in
    tan%282theta%29+=+2tan%28theta%29%2F%281-tan%5E2%28theta%29%29
    and simplify.