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

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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(35256) 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