SOLUTION: 14) If cos y = -4/5 when 90degrees < y < 180degrees, find the value of sin(2y). show work thanks happy new years =)

Algebra ->  Algebra  -> Trigonometry-basics -> SOLUTION: 14) If cos y = -4/5 when 90degrees < y < 180degrees, find the value of sin(2y). show work thanks happy new years =)      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 174693This question is from textbook Amsco's Preparing for the Regents Examination Mathematics B
: 14) If cos y = -4/5 when 90degrees < y < 180degrees, find the value of sin(2y).
show work thanks

happy new years =)This question is from textbook Amsco's Preparing for the Regents Examination Mathematics B

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
If cos y = -4/5, then the adjacent side is 4 units and the hypotenuse is 5 units. So the other leg is sqrt%285%5E2-4%5E2%29=sqrt%2825-16%29=sqrt%289%29=3 units. In other words, this triangle has side lengths of 3, 4, and 5 units.


So sin(y) = opposite/hypotenuse = 3/5


Note: sine is positive since 90 < y < 180



So

sin(2y) = 2*sin(y)*cos(y)


sin(2y) = 2*(3/5)*(-4/5) ... Plug in sin(y) = 3/5 and cos y = -4/5


sin(2y) = -24/25