SOLUTION: given that tan theta=7/24 withtheta in quadrant 3 find sin 2 theta

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

RELATED QUESTIONS
If tan theta= -7/24 and theta is in the second quadrant, find sin theta. (answered by Fombitz)

verify tan theta/2, given tan theta=root 7/3 and theta is in Quadrant... (answered by stanbon)

Find sin (2 theta) Given: csc theta = 9/7, theta is in quadrant... (answered by stanbon)

1.) sin < 0, tan < 0, what quadrant will both be in? 2.) Find the exact value of... (answered by lwsshak3)

If sin (theta)=3/7, And Theta¸ Is In Quadrant II, Then Find cos (theta)= tan... (answered by MathLover1,MathTherapy)

Given that cos theta = -5/13 with theta in quadrant II, find tan 2... (answered by lwsshak3)

Given that tan theta = 15/8 with theta in quadrant I, find cos 2... (answered by lwsshak3)

Find cos(2 theta) Given : tan theta = 12/5, theta is in quadrant... (answered by stanbon)

A) If sinA=-1/25 and angle A terminates in quadrant IV, what does tanA equal? B) Given (answered by Theo,MathLover1,MathTherapy)