*sigh* "Difficult Trig Equation"...?

Question

Can someone show me the steps to solving this? Thank you!

8 cos^2 (theta) - 3 = 1

Thank you all, you are very helpful!

...I wish I could figure these out more easily. Suffice to say math is NOT my subject, Trig even more so!

Answer 1

8 cos ² θ = 4
cos ² θ = 1/2
cos θ = ± 1 / √2
θ = π/4 , 3π/4 , 5π/4 , 7π/4

Answer 2

8cos^2(X)-3=1
8cos^2(X)=4
cos^2(X)=4/8
(cos^2(x))^1/2=(1/2)^1/2
cos(x)=(1/2)^1/2
x=cos((1/2)^1/2)^-1)
x=45 degrees

* I set x equal to theta
* anything raised to 1/2 power is the same as square root
* x is equal to the cosine inverse of the square root of 1/2

Answer 3

8 cos^2 (theta) - 3 = 1
=> 8 cos^2 (theta) = 4
=> cos^2 (theta) = 1/2
=> cos(theta) = +/- 1/sqrt2
=> theta = 45,135, 225, 315 deg

Answer 4

8COS^2(THETA) = 1+3 = 4
cos^(theta) = 4/8 = 1/2
cos(theta) =+- sqrt(1/2)
theta = cos inverse(+-sqrt(1/2))
theta = +-45 degrees

Answer 5

if ur allowed a calculator, it's fairly easy. whenever you want to solve for something you just have to move everything else out of the way, keeping in mind to do the same thing to both sides of the equation.around until you've got it. for instance i would move the 3 over by adding it, then divide both sides by 8 to get rid of that term, then take the square root of booth sides, then take the inverse of that number. the reason i did it in that order is because you usually save the "hardest" things to get rid of last, so adding subtracting is easiest, followed by multiplication and division, followed by powers, followed by cosines and sines.

Answer 6

Add 3 to both sides. Divide both sides by 8. This gets cos^2(θ) on one side. Then take the square root (don't forget the ±) and arccosine.

Answer 7

Ok this is simple. First let x=cos^2(theta)

8x-3=1

So x=0.5

cos(theta) = 0.25 (plus or minus)

Just take the inverse cosine of 0.25 and you get

k + n*pi

Answer 8

you need to isolate Theta
8cos^2(Theta) = 1 + 3
cos^2(theta) = 4 / 8
cos(theta) = sqrt(1/2)
thetha = arccos (sqrt(1/2)) = pi / 4 = 45°

Answer 9

I agree. yet communism replaced into unquestionably based very very like a non secular cult. chief on the proper whom the the remainder of the inhabitants worships. Indoctrination via way of propaganda. in simple terms because of the fact human beings are not non secular does no longer propose they gained't blindly follow different dogmas. it relatively is human nature. EDIT:pheemz, you're an imbecile. Marx in simple terms offered his very own political philosophy. the folk who have been in charge for the killing have been dictators who exploited that philosophy.

Answer 10

8cos^2(th) = 4

cos^2(th) = 0.5

cos(th) = 1/sqrt(2)

th=pi over 4 radians (or 45 degrees)