Solving Trig Equations: 4 More Solutions to Find

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In summary, the four main methods for solving trigonometric equations are factoring, finding common denominators, using trigonometric identities, and substitution. The domain of a trigonometric equation is determined by the values that are allowed for the variable in the equation. Calculators can be a helpful tool when solving trigonometric equations, but their solutions may not always be exact. To check the validity of a solution, it can be substituted back into the original equation or graphed using a calculator. Special cases may arise when solving trigonometric equations, such as inverse trigonometric functions, multiple solutions, and extraneous solutions. Careful analysis and appropriate methods are necessary to solve for all possible solutions.
  • #1
kuahji
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The question is Solve the trig equation for all values of the variable in the first positive rotation.

Problem cos^2 3x = 1

Heres how I attempted to solve the equation

3x = arccos (1)^2

1/3 arccos 1

cos = 0 & 180

However, on the test, the professor stated there were 4 more solutions & I'm having trouble trying to figure them out. What more do I need to do?
 
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  • #2
kuahji said:
3x = arccos (1)^2
This is wrong.cos2(3x) = 1
<=> cos 3x = +- 1
Can you do the rest?
 
  • #3
Yes, thank you. I see what I did now & this helps.
 

1. What are the four main methods for solving trigonometric equations?

The four main methods for solving trigonometric equations are factoring, finding common denominators, using trigonometric identities, and substitution.

2. How do I determine the domain of a trigonometric equation?

The domain of a trigonometric equation is determined by the values that are allowed for the variable in the equation. In general, the domain of a trigonometric equation is all real numbers except for values that would result in undefined expressions, such as dividing by zero or taking the square root of a negative number.

3. Can I use a calculator to solve trigonometric equations?

Yes, calculators can be a helpful tool when solving trigonometric equations. However, it is important to remember that calculators may not always provide exact solutions and may round to a certain number of decimal places.

4. How do I know if my solution to a trigonometric equation is correct?

To check the validity of your solution to a trigonometric equation, you can substitute the value back into the original equation and see if it satisfies the equation. Additionally, you can use a graphing calculator to graph both the original equation and your solution and see if they intersect at the same point.

5. Are there any special cases when solving trigonometric equations?

Yes, there are a few special cases when solving trigonometric equations, such as equations involving inverse trigonometric functions, equations with multiple solutions, and equations with extraneous solutions. It is important to carefully analyze the equation and use appropriate methods to solve for all possible solutions.

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