Question
Find sin 2x if sinx=3/5 and x is in Quadrant II.
Answers
Reiny
sinx = 3/5 = opposite/hypotenuse = y/r
and you are in quad II
make a sketch, you should recognize the 3-4-5 Pythagorean triangle, if not ...
x^2 + y^2 = r^2
x^2 + 9 = 25
x = ± 4, but we are in II , so x = -4
cosx = -4/5
sin (2x) = 2sinxcosx = 2(3/5)(-4/5) = -24/25
check it with a calculator to satisfy your curiosity.
and you are in quad II
make a sketch, you should recognize the 3-4-5 Pythagorean triangle, if not ...
x^2 + y^2 = r^2
x^2 + 9 = 25
x = ± 4, but we are in II , so x = -4
cosx = -4/5
sin (2x) = 2sinxcosx = 2(3/5)(-4/5) = -24/25
check it with a calculator to satisfy your curiosity.