- #1
kieth89
- 31
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Homework Statement
The question is to find [itex]sin 2x, cos 2x, tan 2x[/itex] from the given information: [itex]sin x = -\frac{3}{5}[/itex], x in Quadrant III
Homework Equations
Half Angle Identities
[itex]cos2x = cos^{2}x - sin^{2}x[/itex]
[itex]sin2x = 2sinxcosx[/itex]
[itex]tan2x = \frac{2tanx}{2-tan^{2}x}[/itex]
The Attempt at a Solution
I can find the solution for the most part, the only thing I can't figure out are the signs. What I do is use the given sin[itex](-\frac{3}{5})[/itex] to make a right triangle and solve for the unknown side. I then use that triangle to set up the 3 half angle identities and just plug in the numbers. I can do all that fine, but I can't figure out what should be negative and positive. I thought that since it is in Quadrant 3 both sin2x and cos2x should end up negative. However the back of the book answers say that they are all positive. Why?