How do you make y= sin(sqrt(5x + 3)) in terms of y? :/

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In summary, the conversation is discussing how to move the sine function to the y side and whether it is possible to express it as arcsin(y)=sqrt(5x+3). The speaker also expresses confusion and asks for help with moving the sin function. The final comment provides a general equation for solving the problem, but notes that it is only valid under certain conditions.
  • #1
Lo.Lee.Ta.
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1. Yes, I don't know this. =.=

So how to you move sine to the y side?

You can't say: arcsin(y) = sqrt(5x + 3), can you...?

I don't know how to move the sin!
Help!
Thank you! :)
 
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  • #2
Lo.Lee.Ta. said:
1. Yes, I don't know this. =.=

So how to you move sine to the y side?

You can't say: arcsin(y) = sqrt(5x + 3), can you...?

I don't know how to move the sin!
Help!
Thank you! :)

You can do that as long as you realize it will only be valid for -pi/2<=sqrt(5x+3)<=pi/2.
 
  • #3
Hi Lo.Lee.Ta.! :smile:

Generally, the equation
$$y=sin(\theta)$$
is equivalent to
$$\theta=\arcsin(y)+ 2k\pi \quad \vee \quad \theta=\pi - \arcsin(y) + 2k\pi$$
where ##k## is an integer and ##\theta## is an angle in radians.
 

FAQ: How do you make y= sin(sqrt(5x + 3)) in terms of y? :/

1. How do you find the value of y?

The value of y can be found by plugging in a value for x into the equation y = sin(sqrt(5x + 3)). The resulting value will be the y-coordinate on the graph.

2. Can you explain the function y = sin(sqrt(5x + 3)) in simpler terms?

This function is a combination of two functions: y = sin(x), which represents a sine wave, and y = sqrt(5x + 3), which represents a square root function. The input of x is first multiplied by 5, then 3 is added, and the square root of that value is taken. This value is then used as the input for the sine function, resulting in a shifted and compressed sine wave.

3. How does changing the value of x affect the graph of y = sin(sqrt(5x + 3))?

Changing the value of x will cause the graph to shift horizontally and vertically, as well as change the amplitude and frequency of the sine wave. The graph will also become more compressed as x increases.

4. What is the domain and range of y = sin(sqrt(5x + 3))?

The domain of this function is all real numbers, since any value of x can be plugged into the equation. The range, however, is limited to values between -1 and 1, since the sine function has a maximum amplitude of 1.

5. Can this equation be represented as a graph?

Yes, this equation can be graphed on a coordinate plane. The resulting graph will be a shifted and compressed sine wave, with the x-axis representing the input values and the y-axis representing the output values of y.

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