Calculating tan2x: cosx=12/13, x=[3pi/2, 2pi]

[tahayassen]

Homework Statement

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

Homework Equations

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

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?

 

[sjb-2812]

Homework Statement

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

Homework Equations

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

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?

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?

 

[tahayassen]

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

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

 

[tahayassen]

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

 

[NascentOxygen]

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.