SOLUTION: Find sin(2a) when a terminates in quadrant II. cosa=-4/5. (I got -24/25, but I am not sure if I solved it correctly)

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Question 1174754: Find sin(2a) when a terminates in quadrant II. cosa=-4/5. (I got -24/25, but I am not sure if I solved it correctly)
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

you got it right!

given:
sin%282a%29
cos%28a%29=-4%2F5
when a terminates in quadrant II, 0%3C=+a+%3C=180
use identity:
sin%5E2%28a%29=1-cos%5E2%28a%29.........substitute cos%28a%29=-4%2F5
sin%5E2%28a%29=1-%28-4%2F5%29%5E2
sin%5E2%28a%29=1-%2816%2F25%29
sin%5E2%28a%29=25%2F25-16%2F25
sin%5E2%28a%29=9%2F25
sin%28a%29=sqrt%289%2F25%29
then sin%28a%29+=+3%2F5 or sin%28a%29+=-+3%2F5
use identity:
sin%282a%29=2+sin%28a%29+cos%28a%29+..........substitute sin%28a%29 and+cos%28a%29
note: since a is in quadrant II, the info leads to+sin%28a%29+=++3%2F5,so we have
sin%282a%29=2+%283%2F5%29%28-4%2F5%29
sin%282a%29=-24%2F25

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
Find sin(2a) when a terminates in quadrant II. cosa=-4/5. (I got -24/25, but I am not sure if I solved it correctly)
You are CORRECT!

This is one of the PYTHAG TRIPLES, of the 3-4-5 variety.

And, with  matrix%281%2C3%2C+cos+%28a%29%2C+%22=%22%2C+-+4%2F5%29, OPPOSITE = y = 3 (Quadrant 2), and matrix%281%2C7%2C+sin+%28a%29%2C+%22=%22%2C+O%2FH%2C+%22=%22%2C+y%2Fr%2C+%22=%22%2C+3%2F5%29

We now get: