Sunday

February 1, 2015

February 1, 2015

Posted by **Mark** on Monday, November 14, 2011 at 11:15am.

cos 4x + cos 2x = 0, 0<(or equal to) x < pi

- Trig -
**Reiny**, Monday, November 14, 2011 at 1:33pmuse the identity

cos 2A = 2 cos^2 A - 1 on cos4A

cos 4A = 2cos^2 2A - 1

so

2cos^2 2A - 1 + cos 2A = 0

(2cos 2A -1)(cos 2A + 1) = 0

cos 2A = 1/2 or cos 2A = -1

2A = 60° or 300° or 2A = 180°

A = 30° or 150° or A = 90°

I guess I should have kept x instead of A, no big deal.

x = 30°, 90° , 150°

or

x = π/6, π/2, 5π/6

check:

if x=30° --- cos 120° + cos 60° = -1/2 + 1/2 = 0

if x=90 --- cos 360 + cos 180 = 1 - 1 =0

if x = 150 -- cos 600 + cos 300 = -1/2 + 1/2 = 0

all is good.

- Trig -
**Mark**, Monday, November 14, 2011 at 2:32pmThanks. Makes sense. My problem was I was trying to use another double argument property.

**Answer this Question**

**Related Questions**

Math/trig - Solve the equation in the given Domain: 1-cos theta/ sin theta = ...

Math - Solving for Trig Equations - Solve the following equation for 0 less than...

Math - Solving Trig Equations - Solve each equation for o is less than and/or ...

TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...

Math - Solving Trig Equations - What am I doing wrong? Equation: sin2x = 2cos2x ...

Trig--check answer - Solve the equation of the interval (0, 2pi) cosx=sinx I ...

trig - 2sin(x)cos(x)+cos(x)=0 I'm looking for exact value solutions in [0, 3&#...

Precalculus - Solve Cos^2(x)+cos(x)=cos(2x). Give exact answers within the ...

calculus - find max, min and saddle points of the give function f(x,y)=sin(x)+...

Trigonometry - There is an arbitrary triangle with angles A, B, and C and sides ...