math help, cos^2 x= 0.5,?

Question

heres the problem, it is cos^2 x= 0.5 for angles between 0 and 360 degrees, i would be greatful if anyone could explain how to do this, i dont want the answer as i know it, i just need to be explained how to work it out.

Answer 1

Hi
Cos^2 is like (Cos)^2 or Cos*Cos So you have :
(CosX)=+or - (0.5)^1/2
=>cos x=+ or - ((2)^1/2)/2
or x=45 or 315 For +
and x=135 or 225 For -
So you have 4 answers for this equation and you can check them.

Answer 2

As you should know cos U = 0.5 implies that between 0 and 360
degrees U= 60 deg or 360-60=300 deg
If U = 2x you get 2x= 60==> x=30deg or 2x=300 ==>x=150 deg.
There are certain angles whose trig lines as sin , cos ,ans tg should be known by heart

Answer 3

square root both sides to get only cosx=?
then, find the basic angle which is the inverse cos of 0.5 (meaning: cos^-1 0.5)

since this cos equation is both + and - after being sqaure rooted (cosx = + and - ?), you can use all of the quadrants of trigonometry.

1st quad: All are positive (Basic angle)
2nd quad: Sin is positive (180 degrees - Basic angle)
3rd quad: Tan is positive (180 degrees + Basic angle)
4th quad: Cos is poositive. (360 degrees - Basic Angle)
(you should already have known this since you have learnt trigonometry)

Answer 4

if you can use a calculator, get the square root of both sides. then get the arccos of the square root of 0.5.

cos^2x = (cos x)^2

hope this helps!

Answer 5

first you square root the whole equation and you'll get:

cos x = 0.707 OR cos x = -0.707 (NA)

after that you use the general formula of cosine where

cos A = x
A = 2n(pi) +/- cos-1(x)

so, for your question,
x = 2n(pi) +/- 0.7855 , where n is a positive integer

then just sub in values for n starting from 0,1,2... etc.