Finding x and y components from an angle

In summary, the conversation discusses finding the unit vector in the xy plane at an angle of 131 degrees from the +x axis with a positive y component. The equation cosO=adj/hyp is used, with a final solution of Ax=-0.656 and Ay=0.754. The magnitude of the unit vector is 1 and the z component is 0.
  • #1
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Homework Statement


A unit vector lies in the xy plane, at an angle of 131 degrees from the +x axis, with a positive y component. What is the unit vector?


Homework Equations



cos[STRIKE]O[/STRIKE]=adj/hyp


The Attempt at a Solution



cos131*=adj/hyp
I know that the z component is obviously 0 (xy plane). The x component is negative in order for the angle to be 131*.

So...
-.656=adj/hyp

And...
((sqrt)x^2+y^2)=1 since it's a unit vector.


Basically, I don't know where to go from here. I know the magnitude is 1, and I know what the angle is, but I don't know how to find out the x and y component values. Any help is greatly appreciated.
 
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  • #2
Edit-
I got it. Duh. The hypotenuse has to be 1. Then cos0=Ax, and it's all plugging in stuff from there.
 

1. How do I find the x and y components from an angle?

To find the x and y components from an angle, you can use trigonometric functions such as sine, cosine, and tangent. The x component can be calculated by multiplying the length of the hypotenuse by the cosine of the angle, while the y component can be found by multiplying the length of the hypotenuse by the sine of the angle.

2. What is the purpose of finding x and y components from an angle?

Finding the x and y components from an angle is important in many scientific and engineering applications, such as calculating forces and velocities in a given direction. It is also useful in navigation and mapping.

3. Can I find the x and y components from any angle?

Yes, you can find the x and y components from any angle. Trigonometric functions can be used to calculate the components for acute, obtuse, and right angles.

4. Is there a specific formula for finding x and y components from an angle?

Yes, the formula for finding the x and y components from an angle is x = hypotenuse * cos(angle) and y = hypotenuse * sin(angle), where the angle is measured in radians. If the angle is in degrees, you will need to convert it to radians before using the formula.

5. How can I check if I have correctly found the x and y components from an angle?

You can use the Pythagorean theorem to check if you have correctly found the x and y components from an angle. According to the theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. So, if you square the x and y components and add them together, the result should be equal to the square of the length of the hypotenuse.

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