Solve...........?

Question

Solve cos² x = 1 for 0°≤ x ≤360°

Desperate for help.

Thanks.

Answer 1

"Looks like I am the only one here who actually used trigonometric identities to solve this properly."

Using that identity means that you are solving sin^2x = 0 instead of cos^2 x = 1. How exactly is that an improvement???

cos^2x = 1
cos x = +1 or -1

x = 0, 180, 360

It's not rocket science.

Answer 2

Cos (x) is always between 0 and 1.

Therefore Cos^2(x) will always be between 0 and 1.

You can use the trigonometric identity

Sin^2(x) + Cos^2(x) =1

we solve for Cos^2.. it is

1-Sin^2(x) (which we need the sin term to go to 0)

so Sin^2(x) will only be 0 when x = 0 or 2pi (180) or 360 .



Looks like I am the only one here who actually used trigonometric identities to solve this properly.

IT IS an improvement because it is a lot easier to solve for sin^2=0 . We just need to figure out what will make sin (x)=0
because 0*0 =0

Answer 3

Either cos x = 1 or cos x = -1

for cos x = 1, x = 0 or 360

for cos x = -1, x = 180

Answer 4

cos² x = 1
cos x = ± 1
x = 0° , 180° , 360°

Answer 5

Since : cos² x = 1
So either cos x = 1
Or cos x = -1
i.e. x= 0°,180°,360°

Answer 6

cos² x = 1

use the identity: cos² x = 1/2 + 1/2cos 2x,

thus

1/2 + 1/2cos 2x = 1

1/2cos 2x = 1/2

cos2x = 1

since cos0 = 1

2x = 0

x = 0°

Answer 7

cos^2x = 1
sqrt(cos^2x) = sqrt(1)
+/- cosx = 1
cosx = 1 and cosx = -1

x = 0, 180, 360