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

  • Thread starter Thread starter tahayassen
  • Start date Start date
Join the discussion
Registration is free. Start your own thread to ask a follow-up.
Sign up Log in
4 replies · 6K views
tahayassen
Messages
269
Reaction score
1

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?
 
Last edited:
Physics news on Phys.org

Discussion

tahayassen said:

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?
 
Last edited:
(sinx)^2 = 1 - (cosx)^2
= 1 - (12/13)^2
= -5/13

sin2x = 2sinxcosx
= 2(-5/13)(12/13)
= -120/169
 
Oh finally! No wonder! I can't believe I made that mistake. Thanks!
 
Last edited:
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. :smile: