4cos^2x-3 =0?

Question

0360

Answer 1

4(cosx)^2 - 3 = 0
Add 3 to each side
4(cosx)^2 = 3
Divide both sides by 4
(cosx)^2 = 3/4
Take the square root of each side
cosx = sqrt(3/4) or -sqrt(3/4)
cosx = sqrt(3)/2 or -sqrt(3)/2
x = pi/6, 11pi/6 or 5pi/6, 7pi/6
x = 30, 330 or 150, 210

Answer 2

LHS = (cosx + 3sinx)² = cos² x + 6 cosx sinx + 9 sin² x = 5(cos² x + sin² x) - 4(cos² x - sin² x) + 3 * 2sinx cosx = 5 - 4cos 2x + 3 sin 2x =RHS RHS = 5 - 4cos 2x + 3 sin 2x = a million + 4(a million - cos2x) + 6 sinx cosx = a million + 8sin² x + 6 sinx cosx = a million - sin² x + 9 sin² x + 6 sinx cosx = cos² x + 6 sinx cosx + (3sin x)² = (cos x + 3sin x)² = LHS

Answer 3

I assume you mean "4 cos squared x minus 3 equals 0, for x between angles 0 to 360.

First, bring the constant to the right hand side.

4cos^2(x) = 3

Now, divide by 4

cos^2(x) = 3/4

Now, take the square root of both sides. Whenever you take the square root of both sides in an equation, you ALWAYS have to add "plus or minus" (which I'll denote as +/- ).

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

This reduces to

cos(x) = +/- sqrt(3) / 2

At this point you're dealing with these two equations:
cos(x) = sqrt(3)/2
cos(x) = -sqrt(3)/2

Let's solve the first one. On the unit circle graph, where is cos equal to sqrt(3)/2? The answer to that is at (pi/6) and (11pi/6).
Where is cos equal to -sqrt(3)/2? At 5pi/6 and 7pi/6.

Therefore, our answers are
x = pi/6, 11pi/6, 5pi/6, and 7pi/6

BUT we want them in degrees. To convert to degrees we just multiply each by 180/pi, and we get

x = 30, 330, 150, 210

Answer 4

4cos(x)^2 - 3 = 0
4cos(x)^2 = 3
cos(x)^2 = (3/4)
cos(x) = (sqrt(3)/2)
x = 30°, 150°, 210°, or 330°

Answer 5

4cos^2 x=3
cos^2 x=3/4
cos x=+-3^(1/2)/2
=30,150,210,330

Answer 6

(2cos x-√3)(2cos x+√3)
cos x=±√3/2
x=30º,150º, 210º, and 330º