Solving Equations: Acos(?) & Asin(?)

In summary, the conversation discusses how to find the angle in degrees using the magnitude and components of a vector. The conversation also provides a formula using dot products to find the angle, with specific examples for each axis.
  • #1
jaytm2291
23
0

Homework Statement


http://gyazo.com/f4c02f2a57b24a39dfee575837e0a807.png


Homework Equations


Ax = A cos (?)
Ay = A sin(?)


The Attempt at a Solution


I tried putting the magnitude of x cos (?) but honestly have no idea what to do. Thanks
 
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  • #2
Help?
 
  • #3
Is this a joke?
 
  • #4
You were asked for the angle in degrees, not for the component along that axis. If you know the value of BcosΘ, as well as the value of B, it is no problem to find cosΘ and consequently, Θ itself.

If that doesn't quite click for you, the following approach may be useful as and more instructive for more complicated problems.

Use the properties of the vector dot product to find the answer.

[tex]\vec A \cdot \vec B = |A||B|\cos{\theta}[/tex]
So to find the angle, [tex]\cos{\theta}=\frac{\vec A \cdot \vec B}{|A||B|}[/tex]

In your case, you want to find the angle with the x, y, and z axes respectively. So the vectors you'd need to dot would be, [tex]\vec B \cdot \hat x[/tex], [tex]\vec B \cdot \hat y[/tex] and [tex]\vec B \cdot \hat z[/tex]
 
  • #5
for the help!As a scientist, it is important to approach problems with a systematic and logical mindset. In this case, we are dealing with equations involving the trigonometric functions cosine and sine. Let's start by breaking down the given equations:

Ax = A cos (?)
Ay = A sin(?)

First, we can see that both equations involve a constant value A, which suggests that we are dealing with a problem involving a fixed magnitude or amplitude. Next, we have the trigonometric functions cosine and sine, which are commonly used to represent the relationship between the sides and angles of a right triangle.

In order to solve for ?, we need to isolate the variable on one side of the equation. We can do this by dividing both sides of the first equation by A, and both sides of the second equation by A as well. This gives us:

x = cos (?)
y = sin(?)

Now, we can use the inverse trigonometric functions (arccosine and arcsine) to find the value of ? by taking the cosine and sine of x and y respectively. This will give us the angle that corresponds to the given values of x and y.

Therefore, the solution to the equations would be:
? = arccos(x)
? = arcsin(y)

In summary, when solving equations involving cosine and sine, it is important to recognize the relationship between these functions and right triangles. It is also helpful to use inverse trigonometric functions to find the value of the angle. Keep in mind that there may be multiple solutions for ? depending on the values of x and y. I hope this explanation helps you understand the problem better. Good luck with your homework!
 

1. What is the difference between Acos(?) and Asin(?) equations?

The main difference between Acos(?) and Asin(?) equations is that Acos(?) represents the inverse cosine function, while Asin(?) represents the inverse sine function. This means that Acos(?) calculates the angle whose cosine is the given value, while Asin(?) calculates the angle whose sine is the given value.

2. How do you solve an equation using Acos(?) and Asin(?)?

To solve an equation using Acos(?) and Asin(?), you first need to isolate the function on one side of the equation. Then, use the inverse function (Acos or Asin) to find the angle that corresponds to the given value. Finally, use the unit circle or a calculator to find the actual value of the angle.

3. Can you use Acos(?) and Asin(?) for any value?

No, Acos(?) and Asin(?) can only be used for values between -1 and 1, as these are the possible values for the cosine and sine functions. If the given value falls outside of this range, the equation is not solvable.

4. Are there any special cases when solving equations with Acos(?) and Asin(?)?

Yes, there are two special cases to be aware of when solving equations with Acos(?) and Asin(?). The first is when the given value is 1 or -1, in which case the resulting angle will be 0 or 180 degrees, respectively. The second is when the given value is 0, which will result in an angle of 90 or 270 degrees, depending on whether you are using Acos or Asin.

5. Can you use Acos(?) and Asin(?) to solve for both acute and obtuse angles?

Yes, Acos(?) and Asin(?) can be used to solve for both acute and obtuse angles. However, it is important to remember that the inverse functions (Acos and Asin) only give the principal value, which is the acute angle between 0 and 90 degrees. To find the obtuse angle, you will need to use the properties of the cosine and sine functions to determine the correct angle in the specified quadrant.

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