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

[jaytm2291]

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

 

[jaytm2291]

Help?

 

[jaytm2291]

Is this a joke?

 

[RoyalCat]

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.

$$\vec A \cdot \vec B = |A||B|\cos{\theta}$$
So to find the angle, $$\cos{\theta}=\frac{\vec A \cdot \vec B}{|A||B|}$$

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, $$\vec B \cdot \hat x$$, $$\vec B \cdot \hat y$$ and $$\vec B \cdot \hat z$$

 

[rwisz]

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!