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

Algebra.Com
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)   (Show Source): You can put this solution on YOUR website!
  1. For we have the formula:
  2. For the formula we need
  3. For we need the opposite side, the adjacent side and the quadrant that terminates in. We're given the quadrant.
  4. Since 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 by putting the opposite side, 4, over the adjacent side you just figured out. (And since terminates in the 1st quadrant, we will use the positive ration of opposite over adjacent).)
  7. Take the you just got and put it in the two spots for in

    and simplify.
RELATED QUESTIONS

If sin(theta)= (sqrt2)/5, and pi/2 < theta < pi, then find the exact value of tan(2theta) (answered by lwsshak3)
given sin theta =-1/2 and sec theta >0,find the exact value of tan... (answered by lwsshak3)
give the exact value of cos(theta) and tan(theta) if sin(theta)=(2/5) and 0 (answered by Fombitz)
if sin(theta)=5/6, theta in quadrant 2, find the exact value of tan... (answered by lwsshak3)
Use the given information to find sin 2theta, cos 2theta, and tan 2theta. #1) cos theta (answered by lwsshak3)
Find the exact value of cos(2theta) given csctheta=5/2 and... (answered by stanbon)
Given that tan(theta)=5/4 , pi< theta < 3pi/2, find sin(2theta), cos(2theta),... (answered by lwsshak3)
If cos(theta)=4/5, 0<(theta) (answered by lwsshak3)
If cos theta = - 4/5 and 180degree < theta < 270degree, use trigonometric identities to... (answered by lwsshak3)