#### AKrishan17

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They ask me to find the amplitude of the function 2 sin(4pi*t)+5 cos(4pi*t), in terms of A sin(wt+phi). How do i do this?

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They ask me to find the amplitude of the function 2 sin(4pi*t)+5 cos(4pi*t), in terms of A sin(wt+phi). How do i do this?

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Hi, For a given a rectangle with known width and height, I want to fit 4 circles of equal size regularly (see image) in such a way that the radius of the circles is maximized. The aspect ratio of the rectangle is such that 4 circles fit in the latticed way shown in the image. So the 'most...

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If you are taking a class, I would imagine you have been taught something about this; we'll want to know at least what you have learned that you can use.

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You are given a function:So basically i have this problem that states that

c2 * sin(wt) + c1 * cos(wt) = A * Sin(wt+phi), ............................................(1)

where c2=Acos(Phi) and c1=Asin(Phi).They ask me to find the amplitude of the function 2 sin(4pi*t)+5 cos(4pi*t), in terms of A sin(wt+phi). How do i do this?

2 * sin(4π*t) + 5 * cos(4π*t).................................................................(2)

referring to (1) - for function (2), what are:

c2 = ?

c1 = ?

\(\displaystyle \omega = ? \)

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Correct.

You were told:

c2 =

and

c1 =

Calculate

Hint:

cos

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Somehow i got square root of 29 as A, is that correct?

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Yes. Keep going. Now what is \(\displaystyle \varphi\)?

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30 degrees? or Pi/6?

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I don't really know what i did, but i'm stuck now.

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What do you get when you divide (2) by (1)?c2 =* cos(φ) = 2..................................(1)A

and

c1 =* sin(φ) = 5 .................................(2)A

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2.5

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I asked wrong question. Sorry about that. You have two equations:

and

If you divide equation (2) by equation (1), you will get another equation:

What do you get on the Left-hand-side ?

What do you get on the Right-hand-side ?

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is it equivalent to A tan phi = 5/2?

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Almost - you get:is it equivalent to A tan phi = 5/2?

\(\displaystyle \frac{A}{A} * \frac{\sin(\phi)}{cos(\phi)} = \frac{5}{2}\)

we know A/A = 1, so:

\(\displaystyle \frac{\sin(\phi)}{cos(\phi)} = \frac{5}{2}\)

\(\displaystyle \tan(\phi) = 2.5\)

Now use your calculator and find out the value of \(\displaystyle \phi \).

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I got 1.19? Is this correct?

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1.19 what? degrees? radians? horses? elephants?I got 1.19? Is this correct?

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radians haha!

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So now - how would you answer your posted question?

They ask me to find the amplitude of the function 2 sin(4pi*t)+5 cos(4pi*t), in terms of A sin(wt+phi). How do i do this?