SOLUTION: Find the exact value of the requested trigonometric function of theta. sin theta = -8/9 tan theta >0 Thank you for your time.

Algebra ->  Trigonometry-basics -> SOLUTION: Find the exact value of the requested trigonometric function of theta. sin theta = -8/9 tan theta >0 Thank you for your time.      Log On


   

Question 325199: Find the exact value of the requested trigonometric function of theta.
sin theta = -8/9 tan theta >0
Thank you for your time.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that you want to find the value of tan%28theta%29

Draw a triangle in the third quadrant (since sine is negative, but tangent is positive) and label the two legs to be 'x' and 8. Since the hypotenuse is 9, this means by the pythagorean theorem, we get x%5E2%2B8%5E2=9%5E2. Solve for 'x' to get x=sqrt%289%5E2-8%5E2%29=sqrt%2881-64%29=sqrt%2817%29


Now recall that tangent = opposite/adjacent. In this case, the opposite side is 8 units long and the adjacent side is sqrt%2817%29 units long. So


Or simply put, tan%28theta%29=%288%2Asqrt%2817%29%29%2F17