# math

Solve the equation cos3x=cos2x for 0¡Üx¡Ü360

1. 👍 0
2. 👎 0
3. 👁 139
1. cos3x = cos2x
we need 3(x+2m*pi) = 2(x+2n*pi) for some m and n. Some playing around will get you

x = 0,2/5 pi, 4/5 pi
or, in degrees,
x = 0,144,288

1. 👍 0
2. 👎 0
posted by Steve
2. ?? but the ans is 0, 72 ,144,216,288,360 degree

1. 👍 0
2. 👎 0
posted by Sarah
3. In terms of cosx
cos 3x = 4 cos^3 x - 3cosx , and cos 2x = 2 cos^2 x - 1

so cos 3x = cos 2x
4 cos^3 x - 3cosx - 2cos^2 x + 1 = 0
let cosx = y
so we need
4y^3 - 2y^2 - 3y + 1 = 0

I tried y = 1 and sure enough that was a solution.
then by synthetic division ...
4y^3 - 2y^2 - 3y + 1 = 0
(y-1)((4y^2 + 2y - 1) = 0

y = 1 or y = .30902 or y = -.80902 , using the formula

if y = 1, cosx = 1
x = 0 , 360

if y = .30902 , cosx = .30902
x = 72°, 288

if y = -.80902 , cosx = -.80902
x = 144° , 216°

x = 0, 72, 144, 216, 288, and 360°

1. 👍 0
2. 👎 0
posted by Reiny
4. Good catch, Reiny - I was a bit sloppy.

1. 👍 0
2. 👎 0
posted by Steve

## Similar Questions

1. ### trig--power reducing formulas

Having trouble with this problem: Rewrite the expression as an equivalent expression that does not contain powers greater than 1. Cos³x My answer: cos³x=(cos²x)(cosx) =(1+cos2x/2)(cosx)-->cos+cos³x/2...which is wrong

asked by Brian on April 20, 2009

Solve the equation of the interval (0, 2pi) cosx=sinx I squared both sides to get :cos²x=sin²x Then using tri indentites I came up with cos²x=1-cos²x Ended up with 2cos²x=1 Would the answer be cos²x=1/2???

asked by Brian on April 15, 2009
3. ### Maths

Prove that cos3x/cosx-cos6x/cos2x=2(cos2x-cos4x)

asked by Joel on July 28, 2016
4. ### Math

Solve the equation 2cos2x = √3 for 0°≤x≤360° I did this: cos2x = √3 /2 2x=30 x=15 x=15, 165, 195, 345 Is this correct? Solve the equation √3 sin2x + cos2x = 0 for -π≤x≤π No idea how to approach this one Thanks a

asked by Autumn on October 19, 2017
5. ### math

Solve sin2x + sin4x = cos2x + cos 4x for x in the interval[0,2pi) Hint: the following substitution should come in handy: sin3x= cos3x . tan3x

asked by greg on December 3, 2012
1. ### math

Solve the trigonometric equation from 0¡ã¡Üx¡Ü360 tan⁡x+¡Ì3=0

asked by Anonymous on June 4, 2015
2. ### Precalculus

Please help!!!!!!!!!!! Find all solutions to the equation in the interval [0,2π). 8. cos2x=cosx 10. 2cos^2x+cosx=cos2x Solve algebraically for exact solutions in the interval [0,2π). Use your grapher only to support your

asked by Anonymous on January 3, 2013
3. ### Trig

help please!: (sinx + sin2x +sin3x) / (cosx + cos2x + cos3x) = tan2x

asked by Aiden on March 3, 2013
4. ### Calculus

Solve identity, (1-sin2x)/cos2x = cos2x/(1+sin2x) I tried starting from the right side, RS: =(cos²x-sin²x)/(1+2sinxcosx) =(cos²x-(1-cos²x))/(1+2sinxcosx) and the right side just goes in circle. May I get a hint to start off?

asked by sh on February 27, 2010
5. ### math

Solve the trigonometric equation from 0¡ã¡Üx¡Ü360 tan⁡x+¡Ì3=0 2 sec^2⁡x+tan^2⁡x-3=0

asked by Anonymous on June 4, 2015

More Similar Questions