Unraveling a Tricky Trig Equation: Tips and Tricks for Solving

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In summary, the conversation is about solving a trigonometry equation and the steps involved in doing so. The speaker has factorized the equation and is looking for the next step to solve it. Another person suggests canceling out certain factors and checking for solutions. The conversation ends with the hope that there will be multiple solutions to the equation.
  • #1
mohlam12
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trig equation... :(

Hey everyone,
I have to solve this equation below:
1+cos(x)+cos(2x)=sin(x)+sin(2x)+sin(3x)
After too many simplifications and factorizations, I got to: (I hope it's right tho)

(2sinxcosx)(2cosx+1)=cos(x)(1+2cosx)

So yeah, I factorized everything pretty much, but what step to take after that, so I can solve this equation ??
Thanks,
 
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  • #2
I haven't checked whether your factorization is correct, but assuming it is, you can continue like this: you can cancel out the factors (1+2cosx) and cosx in each side. In order to be allowed to do this, they can't be zero. Check when they are zero and then check whether those values were solutions of the initial problem. After that, all that's left of your equation is 2sinx = 1 which seems easy.
 
  • #3
oh ok, makes sense (sorry i didnt see the canceling out thingy)
thank you!
 
  • #4
No problem, I hope it works out. It seems to me that you'll get quite a number of solutions :smile:
 

1. How do I solve a trigonometric equation?

To solve a trigonometric equation, you need to use the algebraic methods of simplifying and isolating the variable. You may also need to apply trigonometric identities and properties. It is important to have a good understanding of the basic trigonometric functions and their graphs.

2. What is the process for solving a trigonometric equation?

The process for solving a trigonometric equation involves identifying the type of equation and using appropriate methods to simplify and isolate the variable. This may involve factoring, substituting values, or using inverse trigonometric functions.

3. Can you give an example of solving a trigonometric equation?

Sure! Let's say we have the equation sin(x) + 2cos(x) = 1. We can start by using the Pythagorean identity (sin^2(x) + cos^2(x) = 1) to eliminate one of the variables. This gives us 2cos(x) = 1 - cos^2(x). We can then use algebra to simplify and isolate the variable, giving us cos(x) = 1/3. Finally, we can use the inverse cosine function to find the solutions, which are approximately 1.23 and -1.23.

4. What are some common mistakes to avoid when solving trigonometric equations?

Some common mistakes to avoid when solving trigonometric equations include forgetting to check for extraneous solutions, not using the correct trigonometric identity or property, and making arithmetic errors. It is also important to double-check your solutions by plugging them back into the original equation.

5. Are there any tips or tricks for solving tricky trigonometric equations?

One tip is to try converting the equation to only use one type of trigonometric function (e.g. using the Pythagorean identity or double angle formula). You can also try visualizing the equation on a unit circle or graphing it to better understand the solutions. Additionally, practicing and becoming familiar with various trigonometric identities and properties can make solving equations easier.

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