vector A has a magnitude of 45.0 cm and makes an angle of 125 degrees with positive a –axis. What are the x- and y- components of this vector?
I assume you are measuring angles positive counterclockwise
x=45cosine125
y=45sine 125
To find the x- and y-components of a vector, we can use trigonometry. Here's how you can do it:
1. Identify the given information:
- Magnitude of vector A: 45.0 cm
- Angle with the positive x-axis: 125 degrees
2. Determine the x-component:
- The x-component of A can be found using the formula: Ax = A * cos(angle)
- Substitute the values into the formula: Ax = 45.0 cm * cos(125 degrees)
- Use a scientific calculator to find the cosine of 125 degrees: cos(125) ≈ -0.5736
- Calculate the x-component: Ax ≈ 45.0 cm * (-0.5736)
- The x-component of vector A is approximately -25.81 cm.
3. Determine the y-component:
- The y-component of A can be found using the formula: Ay = A * sin(angle)
- Substitute the values into the formula: Ay = 45.0 cm * sin(125 degrees)
- Use a scientific calculator to find the sine of 125 degrees: sin(125) ≈ 0.8192
- Calculate the y-component: Ay ≈ 45.0 cm * 0.8192
- The y-component of vector A is approximately 36.86 cm.
Therefore, the x-component of vector A is approximately -25.81 cm, and the y-component of vector A is approximately 36.86 cm.