Solving Sin() Function Problem: f(x) = 9 sin 7x, g(x) = 18 sin(7x + 5)

In summary, the conversation discusses the functions f(x) = 9 sin 7x and g(x) = 18 sin(7x+5). It is mentioned that g(x) is twice the amplitude of f(x) and has a shift of 5 units. The importance of understanding the factors in the function f(x) = A*sin(Bx+C)+D is emphasized. It is also mentioned that to find the shift between g(x) and f(x), the function g(x) can be rewritten as 2f(x-h) or 18 sin(7x-5) = 2*9 sin(7(x-h)). The value of h can then be determined to make these expressions equal.
  • #1
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82
0
f(x) = 9 sin 7 x, and g(x) = 18 sin(7 x + 5)

so, i assume by looking just like this g(x) is twice much more than f(x) and 5 units more, correct??
 
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  • #2


What do you mean by twice much more and 5 units more? You need to figure out what each of the factors in f(x) = A*sin(Bx + C) + D does, for example, A is the amplitude, 2pi/B is the period, now think as to what C and D are.
 
  • #3


Thanks.
 
  • #4


If you're wondering how much the g(x) is shifted relative to f(x), it's not 5 units. But yes, the amplitude is twice as much.

To get the shift, rewrite g(x) as

g(x) = 2f(x-h)

or

18 sin (7x - 5) = 2*9 sin(7(x-h))

What mus h be, to make those expressions equal?
 

What is the Sin() function?

The Sin() function is a mathematical function that calculates the sine of an angle. It is commonly denoted as Sin(x), where x is the angle in radians.

What is the domain and range of the Sin() function?

The domain of the Sin() function is all real numbers, while the range is between -1 and 1.

Why is the Sin() function useful?

The Sin() function is useful in many areas of mathematics and science, including trigonometry, physics, and engineering. It is used to model periodic phenomena such as sound waves and electromagnetic waves.

What is the relationship between the Sin() function and other trigonometric functions?

The Sin() function is closely related to other trigonometric functions such as Cosine (Cos), Tangent (Tan), and Cosecant (Csc). These functions are all interrelated through various identities and can be used to solve a variety of mathematical problems.

How do you solve a Sin() function problem?

To solve a Sin() function problem, you first need to determine the given angle in radians. Then, you can use a calculator or a table of values to find the corresponding sine value. You can also use trigonometric identities and equations to simplify the problem and find the solution.

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