Question 888977: given that tan theta=7/24 withtheta in quadrant 3 find sin 2 theta
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! tan(theta) = 7/24
tan is equal to sin/cos.
since the angle is in quadrant 3, sine and cos are minus.
this makes tan(theta) = -7/-24.
use the quadratic formula to find the hypotenuse which is equal to 25.
couple of ways to solve this.
first way is to use the sin(2T) formula.
that formula says sin(2T) = 2 * sin(T) * cos(T).
sin(T) = -7/25
cos(T) = -24/25
2 * sin(T) * cos(T) = 2 * -7/25 * -24/25 which is equal to -336 / 625 which has a decimal equivalent of .5376.
second way is to find the angle and then double it and then take the sign of that doubled angle.
since tan(theta) = 7/24, use your calculator to find theta = 16.26020471.
that's in the first quadrant.
in the third quadrant, the angle is 180 + 16.26020471 = 196.26020471.
double that to get 392.5204094.
use your calculator to get sin(392.5204094) = .5376
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