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

In summary, the equation cos2x + cos x = 0 (0 <= x <= 360) has three possible values for x: 60 degrees, 180 degrees, and 300 degrees. The equation can also be solved by using the identity cos2x = 2cos^2(x) - 1 and solving the resulting quadratic equation. It is important to use parentheses when writing math expressions as text to avoid confusion.
  • #1
Helly123
581
20

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?
 
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  • #2
Helly123 said:
cos2x + cos x = 0 (0 <= x <= 360)
Is it cos(2x) or cos2x?
 
  • #3
cnh1995 said:
Is it cos(2x) or cos2x?
it's cos2x
 
  • #4
Helly123 said:
it's cos2x
Of course:-p!
I hadn't read your complete solution.

But I think you've found all the possible values for x.
 
  • #5
cnh1995 said:
Of course:-p!
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
 
  • #6
Check the 270...
 
  • #7
BvU said:
Check the 270...
I see, I get it. thanks
 
  • #8
Helly123 said:

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°?
 
  • #9
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}##
 
  • #10
ehild said:
What about 300°?
Yes, that's the answer
 
  • #11
Chestermiller said:
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
 
  • #12
Helly123 said:
cos2x + cos x = 0 (0 <= x <= 360)

cnh1995 said:
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.
 
  • #13
Mark44 said:
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
 

1. How do I identify the type of trigonometric equation?

To identify the type of trigonometric equation, first look for any trigonometric functions (sine, cosine, tangent, etc.) and constants (numbers) in the equation. Then, determine if the equation is linear (only one trigonometric function), quadratic (trigonometric function raised to the power of 2), or a combination of trigonometric functions.

2. What are the steps to solve a linear trigonometric equation?

The steps to solve a linear trigonometric equation are:

  1. Isolate the trigonometric function on one side of the equation.
  2. Use inverse trigonometric functions to solve for the variable inside the trigonometric function.
  3. Check for extraneous solutions, if necessary.

3. How do I solve a quadratic trigonometric equation?

To solve a quadratic trigonometric equation, follow these steps:

  1. Use trigonometric identities to rewrite the equation in terms of one trigonometric function (usually sine or cosine).
  2. Apply the quadratic formula to solve for the variable inside the trigonometric function.
  3. Check for extraneous solutions, if necessary.

4. What are the common trigonometric identities used to solve equations?

Some common trigonometric identities used to solve equations include:

  • Pythagorean identities: sin²x + cos²x = 1
  • Double angle identities: sin2x = 2sinx*cosx, cos2x = cos²x - sin²x
  • Sum and difference identities: sin(x ± y) = sinxcosy ± cosxsiny, cos(x ± y) = cosxcosy ∓ sinxsiny

5. What should I do if I encounter an equation with multiple trigonometric functions?

If an equation has multiple trigonometric functions, use trigonometric identities to rewrite the equation in terms of one trigonometric function. Then, follow the steps for solving a linear or quadratic trigonometric equation. It may also be helpful to draw a unit circle or use a trigonometric table to solve for the variables.

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