Convert harmonic equation to polar form

In summary, the conversation is about converting the expression cos(7t) + sin(7t) into polar form of Acos(\omega_0 t - \delta). The person asking the question is looking for a website tutorial to learn the process of conversion and does not expect someone to answer it for them. They mention a trig identity that could be useful, but are unsure of how to apply it. Another person gives the advice to let Acos(\theta-\delta)=cos(7t)+sin(7t) and solve for the amplitude, period, and delay.
  • #1
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Homework Statement



Convert
[tex] cos(7 t) + sin(7 t)[/tex]
into polar form of
[tex]A cos(\omega_0 t - \delta)[/tex]

This is a review problem where once we convert this to polar form we are to give amplitude, period and delay (shift). I can answer this question if someone can point me to a website tutorial that tells the process of converting this problem. I really don't expect someone to answer this for me because I need to learn how to do it on my own.


The Attempt at a Solution



I have not made an attempt as of yet, however i know there is a trig identity
cos(x)cos(y) + sin(x)sin(y) = cos(x-y)

I was given this advice BUT I don't know what to do because:
cos(7)cos(t) doesn't equal cos(7t) ... right?
 
Last edited:
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  • #2
Let [itex]Acos(\theta-\delta)=cos(7t)+sin(7t)[/itex] then just equate and solve
 

1. What is a harmonic equation?

A harmonic equation is a mathematical equation that represents a harmonic function, which is a function that repeats itself in regular intervals. It is commonly used in physics and engineering to describe oscillating systems.

2. What does it mean to convert a harmonic equation to polar form?

Converting a harmonic equation to polar form means expressing the equation in terms of polar coordinates, where the variables represent a distance and an angle from a fixed point. This form is particularly useful for describing circular or rotational motion.

3. How do you convert a harmonic equation to polar form?

To convert a harmonic equation to polar form, you can use the substitution method. Replace the x and y variables with rcosθ and rsinθ, respectively. Then, use trigonometric identities to simplify the equation and eliminate any remaining x and y terms.

4. What are the advantages of using polar form for a harmonic equation?

Polar form allows for a more intuitive and geometric interpretation of the equation, making it easier to visualize and understand the behavior of the function. It is also useful for solving problems involving circular or rotational motion, as it simplifies the calculations.

5. Can any harmonic equation be converted to polar form?

Yes, any harmonic equation can be converted to polar form as long as it is expressed in terms of x and y. However, the resulting polar equation may not always be in the simplest form and may require further manipulation to fully utilize its benefits.

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