Trigonometric equations, help? ^^

[Wholewheat458]

Homework Statement

2 cos^2 x + cos x = 0
and
tan x = 3^1/2

Homework Equations

.. ?? Unit circle.

The Attempt at a Solution

for the first, well I tried factoring to isolate x, but it really did not work
i keep making up my own rules that end up messing with the entire equation,
i know, its not the best method
with the second, i used the unit circle (cos, sin) and the principal
that tan is = to sin/cos, but none of them are equal to the square root of 3..oy
any help would be much appreciated ^^
:shy:

 

[tiny-tim]

2 cos^2 x + cos x = 0
and
tan x = 3^1/2

Hi Wholewheat458!

(have a square-root: √ )

There's lots of ways of doing this.

Divide the first equation by cosx … that gives you cos x = 0 or -1/2.

Use sec²x = tan²x + 1 … that gives you cosx = ±1/2.

And you do know an angle with cosx = 1/2, don't you?

 

[Architeuthis Dux]

I would first like to commend you for attempting to solve these trigonometric equations on your own. It shows that you are actively trying to understand the concepts and are not afraid to ask for help when needed.

For the first equation, it is important to remember that factoring is not always the best method for solving trigonometric equations. In this case, we can use the trigonometric identity cos^2 x + sin^2 x = 1 to rewrite the equation as 2(1-sin^2 x) + cos x = 0. This can then be simplified to 2sin^2 x + cos x - 2 = 0. From here, we can use the quadratic formula to solve for sin x and then use the inverse sine function to find the value of x.

For the second equation, it is helpful to remember that the square root of 3 can also be written as the sine or cosine of a specific angle. In this case, we can use the unit circle to find that the angle whose tangent is equal to the square root of 3 is pi/3 radians or 60 degrees.

I hope this helps you in solving these equations. Remember to always double check your solutions and use multiple methods if needed. Good luck!