Simplify Sinusoidal Function 2sin(wot+45)+cis(wot) to Acos(wot)

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In summary, simplifying a function in mathematics means to write it in a more concise and manageable form without changing its value. A sinusoidal function is a mathematical function represented by a sine or cosine curve and commonly used to model periodic phenomena. The number 2 in 2sin(wot+45) represents the amplitude of the function, which is 2 units. "cis" stands for "cosine + i sine" and is used to simplify complex numbers, representing the phase shift of the function as 0 degrees. To convert the function to Acos(wot), we can use the trigonometric identity cos(x+y) = cos(x)cos(y) - sin(x)sin(y) and simplify to get Acos(w
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noname1
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2sin(wot+45)+cis(wot) to Acos(wot)

i convert it

2e^-j45 = √2/2 - j√2/2
1e^j0 = 1 - j0

adding these up i get

(√2/2 + 1) -j(√2/2)

1.707 - j.707

magnitude = √1.707²+.707² = 1.85

angle = tan^-1(.707/1.707) = 22.5

so i get 1.85cos(wot +22.5)

while the book has the answer

2.798cos(wot-30.36)
 
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nevermind i found my issue forgot to multiply the amplitude
 

1. What does the term "simplify" mean in this context?

In mathematics, simplifying a function means to write it in a more concise and easily manageable form, without changing its overall meaning or value.

2. What is a sinusoidal function?

A sinusoidal function is a mathematical function that can be represented by a sine or cosine curve. It is commonly used to model periodic phenomena, such as the motion of a pendulum or the changing tides.

3. What is the significance of the number 2 in 2sin(wot+45)?

The number 2 is known as the amplitude of the sinusoidal function, and it represents the maximum distance between the curve and its midline. In this case, the amplitude is 2 units.

4. What is the meaning of "cis" in cis(wot)?

"cis" is a mathematical function that stands for "cosine + i sine" and is used to simplify complex numbers. In this context, it represents the phase shift of the sinusoidal function, which is 0 degrees.

5. Can you explain how to convert this function to Acos(wot)?

To convert the given function to Acos(wot), we can use the trigonometric identity cos(x+y) = cos(x)cos(y) - sin(x)sin(y). Applying this, we get 2sin(wot+45) + cis(wot) = 2cos(45)sin(wot) + cos(wot) - isin(wot). Simplifying further, we get 2sqrt(2)sin(wot) + cos(wot) - isin(wot), which can be written as Acos(wot) with A = sqrt(2).

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