Trig: tan2x=(-24/7), find sinx and cosx

[carly]

If tan2x=(-24/7), find the exact value(s) of sinx and cosx


Working out the answers by hand, I get

sinx = ±3/5, ±4/5
cosx = ±3/5, ±4/5


But by actually calculating x and plugging it into sinx and cosx, I get

sinx = 3/5, 4/5
cosx = 3/5, -4/5


I'm pretty sure that the latter are the answers, but how do I justify it given the ±?

 

[stapel]

If tan2x=(-24/7), find the exact value(s) of sinx and cosx

Working out the answers by hand, I get

sinx = ±3/5, ±4/5
cosx = ±3/5, ±4/5

How did you arrive at these values? (It is a bit difficult to check work that we cannot see. If you show your work, rather than mentioning the results of it, we usually can provide more-helpful replies.)

Note: If the tangent of an angle is negative, then the angle must be in the second or fourth quadrant. Since 2x is in the second or fourth quadrant, then 3pi/4 < 2x < 2pi or 0 < x < pi/2. Then 3pi/8 < x < pi or 0 < x < pi/4. What would be the signs on sines and cosines within these intervals?

Eliz.