# Calculate tan2x

1. Dec 12, 2011

### tahayassen

1. The problem statement, all variables and given/known data

cosx=12/13
3pi/2 is less than or equal to x is less than or equal to 2pi

2. Relevant equations

sin2x = 2sinxcosx
cos2x = 1-2(sinx)^2
tan2x = (2tanx)/(1-(tanx)^2)

3. The attempt at a solution

Using the tan2x formula, I get -60/47. Using the sin2x (sin2x=-120/169) and cos2x (cos2x=119/169) formulas, than dividing sin2x by cos2x, I get -120/119.

tan2x=2(-5/12)/(1-2(-5/12)^2)
=(-10/12)/47/72
=-60/47

Why am I getting different values?

Last edited: Dec 12, 2011
2. Dec 12, 2011

### sjb-2812

How have you calculated sin 2x, this looks wrong to me.
oops, my bad. Why are you multiplying tan x by two in the denominator for the tan 2x formula?

Last edited: Dec 12, 2011
3. Dec 12, 2011

### tahayassen

(sinx)^2 = 1 - (cosx)^2
= 1 - (12/13)^2
= -5/13

sin2x = 2sinxcosx
= 2(-5/13)(12/13)
= -120/169

4. Dec 12, 2011

### tahayassen

Oh finally! No wonder! I can't believe I made that mistake. Thanks!

Last edited: Dec 12, 2011
5. Dec 12, 2011

### Staff: Mentor

Use your calculator to find the value of x. Then use it to find tan of double that angle. Now you can figure which of your algebraic answers is wrong.