- #1
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Homework Statement
I want to express sin(x) in terms of tan(x).
Homework Equations
tan(x)=sin(x)/cos(x)
1+tan2(x)=sec2(x)
The Attempt at a Solution
sin(x)=cos(x)tan(x)
At this point I realize this is assuming [itex]x\neq \pi/2+k\pi[/itex]
[tex]cos^2(x)=\frac{1}{1+tan^2(x)}[/tex]
therefore, [tex]sin(x)=\frac{tan(x)}{\sqrt{1+tan^2(x)}}[/tex]
But I graphed this and it only looks right half of the time. What I should have is the plus or minus when taking the root of cos2(x) but I need the plus half the time, and the minus the other half of the time and then merge them to describe sin(x) in terms of tan(x).
How should I go about this problem and realize what must be done without the use of graphing tools.