What is x in this trig equation... sin^2(x) = 3cos^2(x)?

Question

The carrot symbol represents that sine and cosine are both squared.

Answer 1

sin^2(x) = 3cos^2(x)
sin^2(x) + cos^2(x) = 4cos^2(x)
1 = 4cos^2(x)
1/4 = cos^2(x)
+/- 1/2 = cos(x)

cos(+/- 60 degrees) = 1/2
cos(+/- 120 degrees) = -1/2

So, we have -120, -60, 60, and 120 degrees. (Or if you prefer radians between -pi and pi: -2pi/3, -pi/3, pi/3, 2pi/3. And between 0 and 2pi: pi/3, 2pi/3, 4pi/3, 5pi/3.)

Answer 2

I see that you have posted a number of trig equations. Almost all of them are based on using one or more of the trig formulae. In this case the task is to turn sinx into cosx or vice versa. This question has squares in it so we make use of cos² x + sin² x = 1

sin² x = 3cos² x

1 - cos² x = 3cos² x

1 = 4cos² x

1/4 = cos² x

cosx = ± ½

x = 60, 300, ...... or 120, 240... adding 360 to get further values

Answer 3

divide the sine squared function by the cos squared function.
that gives

sin^2(x) / cos^2(x) = 3.
now sin(x)/cos(x)= tan (x)
so that gives
tan^2(x)=3
or
tan(x)=square root 3
that yields x= 60 degrees or pi/3 radians
a more accurate answer is
x= pi/3 +or- n times pi
since the tan function is periodic with a period of pi.

Answer 4

sin^2(x) = 3cos^2(x)
Divide both sides by cos629x)
tan^2(x)=3
tan(x)=sqrt(3)
x = pi/3 + n.pi

Answer 5

as cos x is not zero devide by cos ^ 2 x

tan^2 x = 3

tan x = +/-sqrt(3)

x = pi/3 or 2pi/3 or 4pi/3 or 5pi/3 or npi added to it

Answer 6

x is the unknown you have to solve for.



Joking aside divide both sides by cos^2x and you get tan^2x =3

So what does tanx = ? So what then is x?

Answer 7

sin^2(x) = 3cos^2(x)or
tan^2x=3
tanx=sqrt(3).
x=pi/3,7pi/3. answer