Posted by **Sandy** on Sunday, June 6, 2010 at 11:19pm.

solve for x if x is in radians.

cos2(x) + 4cos(x) = -3

- trig -
**Reiny**, Sunday, June 6, 2010 at 11:24pm
Is that

cos^2 x + 4cosx = -3 ??

if so, then let cosx = y to get

y^2 + 4y + 3 = 0

(y+1)(y+3) = 0

y = -1 or y = -3

so

cosx = -1 ---> x = π

or

cosx = -3 , not possible

so x = π

- trig -
**Sandy**, Sunday, June 6, 2010 at 11:27pm
no, its not squared. it is (cosx)(2)

- trig -
**Reiny**, Sunday, June 6, 2010 at 11:42pm
(cosx)(2) wouldn't make much sense, then it would be

2cosx and the entire equation would be

6cosx = -3

cosx = -1/2

and x = 120° or 240°

did you mean cos(2x) ?

then you can use the identity

cos(2x) = 2cos^2x - 1

cos((x) + 4cos(x) = -3

2cos^2x - 1 + 4cosx = -3

2cos^2x + 4cosx + 2 = 0

cos^2x + 2cosx + 1 = 0

(cosx + 1)^2 = 0

cosx + 1 = 0

cosx = -1

x = 180° or x = π

(which by coincidence is the same answer to the other interpretation)

- trig -
**Sandy**, Sunday, June 6, 2010 at 11:49pm
okay i think that is right. thank you

## Answer This Question

## Related Questions

- Math - Trig - Double Angles - Prove: cos4x = 8cos^4x - 8cos^2x + 1 My Attempt: ...
- Trig 3 - Why does 1 - COS2(Squared) _________________ COS2 = tan2
- trig - cos2(120degrees) help me solve this please
- trig - solve for exact value for x between 0 and 2 pie 3sin2(x)-cos2=2?
- Math - Trig - Solve for exact or to 1d.p of x E [0 ,2pi] 4cos^2x-3
- Maths - if in a triangle ABC m angle A=π/2, then value of cos2 A + cos2 B...
- maths - If S=1/2^2cos1 + 1/cos1¤cos2+1/2^3 cos1 ¤cos2¤cos2^2 + .......... upto ...
- trig - Write an equation for simple harmonic motion, given that the amplitude ...
- Math/Trig - Solve: 2 cos2 x - 3 cos x + 1 = 0 for 0 is less than or equal to x ...
- trig - Solve rounding to 2 decimal places. 9cosx + 4cos(2x) + 1 = 0 over 0° &#...

More Related Questions