What Are the Solutions for cos(2x) + cos(x) = 0?

[Helly123]

Homework Statement

cos2x + cos x = 0 (0 <= x <= 360)

Homework Equations

The Attempt at a Solution

cos2x + cos x = 0
2cos(3x)/2 cos(x)/2 = 0

3x/2 = 90 degrees
x = 60 degrees

x/2 = 90
x = 180

3x/2 = 270
x = 180

x/2 = 270
x = 540 (not qualified)

is there any more possibility (answers) for x?

 

[cnh1995]

cos2x + cos x = 0 (0 <= x <= 360)

Is it cos(2x) or cos²x?

 

[Helly123]

Is it cos(2x) or cos²x?

it's cos2x

 

[cnh1995]

it's cos2x

Of course!
I hadn't read your complete solution.

But I think you've found all the possible values for x.

 

[Helly123]

Of course!
I hadn't read your complete solution.

But I think you've found all the possible values for x.

thank you. But there's one more answers but I don't know how to find it

 

[BvU]

Check the 270...

 

[Helly123]

Check the 270...

I see, I get it. thanks

 

[ehild]

Homework Statement

cos2x + cos x = 0 (0 <= x <= 360)

Homework Equations

The Attempt at a Solution

cos2x + cos x = 0
2cos(3x)/2 cos(x)/2 = 0

3x/2 = 90 degrees
x = 60 degrees

x/2 = 90
x = 180

3x/2 = 270
x = 180

x/2 = 270
x = 540 (not qualified)

is there any more possibility (answers) for x?

What about 300°?

 

[Chestermiller]

Why didn't you just write $$\cos{2x}=2\cos^2{x}-1$$and then directly solve the resulting (factorable) quadratic equation for $\cos{x}$

 

[Helly123]

What about 300°?

Yes, that's the answer

 

[Helly123]

Why didn't you just write $$\cos{2x}=2\cos^2{x}-1$$and then directly solve the resulting (factorable) quadratic equation for $\cos{x}$

I see.. I didn't realize it

 

[Mark44]

cos2x + cos x = 0 (0 <= x <= 360)

Is it cos(2x) or cos²x?

To prevent such confusion, use parentheses -- i.e., write cos(2x) instead of cos2x. Also, we get a lot of students who are new to writing math expressions as text. I've seen many who write cos2x when they really mean cos²(x). For exponents, the ^ symbol is often used.

 

[Helly123]

To prevent such confusion, use parentheses -- i.e., write cos(2x) instead of cos2x. Also, we get a lot of students who are new to writing math expressions as text. I've seen many who write cos2x when they really mean cos²(x). For exponents, the ^ symbol is often used.

Ok I'll be more careful