Trouble Simplifying Homework Equations

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In summary, the conversation discusses a problem with simplifying a trigonometric equation from the first to the second equation. The relevant trig identity is provided and further steps are explained in order to solve the problem.
  • #1
ACLerok
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Homework Statement


I am reviewing some old exam solutions and came across something I cannot figure out. I'm don't understand how they simplify from the first equation to the second. I looked up a table of trig identies but could not find anything that would help.


Homework Equations


http://img296.imageshack.us/img296/864/untitledimageda3.th.jpg


The Attempt at a Solution

 
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  • #2
Expand cos ( theta + pi/4), and times it by root 2.
 
  • #3
The relevant trig identity is [itex]cos(\theta+ \phi)= cos(\theta)cos(\phi)- sin(\theta)sin(\phi)[/itex]

Ignoring the 'm(t)' which just "goes along for the ride", you have [itex]2cos(\theta)- 2 sin(\theta)[/itex]. Obviously, since 2> 1, there is no [itex]\phi[/itex] that has both sine and cosine equal to 2- you will need divide by something. But you would still have [itex]cos(\phi)= sin(\phi)[/itex]. What value of [itex]\phi[/itex] has that property? And what do you then need to divide by?
 

Related to Trouble Simplifying Homework Equations

1. Why is it important to simplify homework equations?

Simplifying equations helps to make them easier to understand and work with. It also allows for more efficient problem solving and can help identify mistakes or errors in calculations.

2. What strategies can I use to simplify homework equations?

Some strategies for simplifying equations include combining like terms, factoring, and using the order of operations. It is also helpful to break down the equation into smaller parts and identify any patterns or relationships.

3. How can I check if my simplified equation is correct?

One way to check the accuracy of a simplified equation is to plug in values for the variables and see if the equation holds true. Another method is to work backwards and see if the original equation can be created from the simplified version.

4. What should I do if I am still having trouble simplifying an equation?

If you are struggling to simplify an equation, it can be helpful to ask for assistance from a teacher, tutor, or classmate. You can also try breaking the equation down into smaller parts or using online resources for additional practice and explanations.

5. Are there any common mistakes to watch out for when simplifying equations?

Yes, some common mistakes include forgetting to distribute negative signs, combining unlike terms, and incorrectly applying the order of operations. It is important to double check your work and be mindful of any potential errors.

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