- #1

2thumbsGuy

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I'm trying to find where x = 0 in this equation: sin((x-10)^2)

I forget how this works. Can I get a little help?

Thank you!

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- Thread starter 2thumbsGuy
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In summary, the conversation discussed finding the values of x that make the expression sin((x-10)^2) equal to 0. Solutions were provided by recognizing that sin(A) equals 0 when A is any integer multiple of pi, and that the solution to the equation sin((x-10)^2) = 0 is (x-10)^2 = kpi, where k is any integer. The conversation also mentioned potential confusion caused by working with more complex expressions and using excel for calculations.

- #1

2thumbsGuy

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I'm trying to find where x = 0 in this equation: sin((x-10)^2)

I forget how this works. Can I get a little help?

Thank you!

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- #2

SteamKing

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You have an expression, not an equation.2thumbsGuy said:

I'm trying to find where x = 0 in this equation: sin((x-10)^2)

I forget how this works. Can I get a little help?

Thank you!

Are you instead trying to find out the values of x which make sin ((x-10)

- #3

2thumbsGuy

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Right, yes! That!

- #4

phion

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- #5

Mark44

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There's no advantage in expanding (x - 10)phion said:

- #6

2thumbsGuy

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So, x = (√(nπ) + 10)? So then where does arcsin come in?

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SteamKing

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sin ((x- 10)2thumbsGuy said:So, x = (√(nπ) + 10)? So then where does arcsin come in?

arcsin [sin ((x-10

(x - 10)

x - 10 = √(nπ)

x = √(nπ) + 10

How about that?

- #8

Mark44

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Make that ##x - 10 = \pm\sqrt{n\pi}## and I'll be happy.SteamKing said:sin ((x- 10)^{2}) = 0

arcsin [sin ((x-10^{2})] = arcsin (0)

(x - 10)^{2}= nπ, where n = 0, 1, 2, 3, ...

x - 10 = √(nπ)

SteamKing said:x = √(nπ) + 10

How about that?

- #9

2thumbsGuy

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aaaaaaah nice, it's kind of coming trickling back, now. Thank you, sirs!

- #10

2thumbsGuy

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arcsin [sin ((x-10

How does arcsin(0) equal anything but 0?

- #11

Mark44

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It doesn't. In my opinion you'll just confuse yourself by invoking arcsin.2thumbsGuy said:

arcsin [sin ((x-10^{2})] = arcsin (0) = (x - 10)^{2}= nπ ...?

How does arcsin(0) equal anything but 0?

You're trying to solve the equation ##\sin((x - 10)^2) = 0##. The easiest way to solve this is to recognize that sin(A) = 0 when A is any integer multiple of ##\pi##, so the solution of this equation is ##A = k\pi##, where k is any integer. Look at a graph of y = sin(x) to see this.

Going back to your equation, you have ##\sin((x - 10)^2) = 0##, so it must be that ##(x - 10)^2 = k\pi##, with k again being any integer. Can you solve this equation for x now?

- #12

2thumbsGuy

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Many thanks!

The purpose of solving for x = 0 is to find the value of x that makes the equation true. This is known as the "root" or "solution" of the equation.

There are several methods for solving equations with x = 0, including substitution, elimination, and graphing. Each method may be more suitable for certain types of equations.

Some common mistakes to avoid when solving for x = 0 include forgetting to check for extraneous solutions, making arithmetic errors, and not following the correct order of operations.

You can check your solution for x = 0 by plugging it back into the original equation and seeing if it makes the equation true. You can also use a graphing calculator to visualize the solution.

Solving for x = 0 is a fundamental skill in mathematics and has many real-life applications. It can be used to solve problems in finance, physics, engineering, and many other fields where equations are used to model and solve real-world problems.

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