A vector has a magnitude of 17.6 cm and makes an angle of 150.0° with the positive x-axis. What are the x- and y-components of this vector?
To find the x- and y-components of the vector, we can use trigonometry.
The x-component can be determined using the cosine of the angle:
x-component = magnitude * cos(angle)
x-component = 17.6 cm * cos(150.0°)
Using the unit circle, we know that cos(150.0°) is equal to -cos(30.0°). Therefore:
cos(150.0°) = -cos(30.0°)
x-component = 17.6 cm * (-cos(30.0°))
We can use the known value of cos(30.0°) ≈ 0.866:
x-component = 17.6 cm * (-0.866)
x-component ≈ -15.20 cm
The y-component can be determined using the sine of the angle:
y-component = magnitude * sin(angle)
y-component = 17.6 cm * sin(150.0°)
Using the unit circle, we know that sin(150.0°) is equal to sin(30.0°):
sin(150.0°) = sin(30.0°)
y-component = 17.6 cm * sin(30.0°)
We can use the known value of sin(30°) = 0.5:
y-component = 17.6 cm * 0.5
y-component = 8.80 cm
Therefore, the x-component of the vector is approximately -15.20 cm and the y-component is 8.80 cm.
To find the x- and y-components of a vector, we need to use trigonometry. The magnitude of the vector, 17.6 cm, represents the hypotenuse of a right triangle.
The x-component is the length of the side adjacent to the angle, and the y-component is the length of the side opposite to the angle.
To find the x-component, we can use cosine:
cos(angle) = adjacent / hypotenuse
cos(150.0°) = x-component / 17.6 cm
To find the y-component, we can use sine:
sin(angle) = opposite / hypotenuse
sin(150.0°) = y-component / 17.6 cm
Now let's calculate the x- and y-components:
x-component = cos(150.0°) * 17.6 cm
y-component = sin(150.0°) * 17.6 cm
Calculating these values, we get:
x-component = -14.3 cm
y-component = 8.8 cm
Therefore, the x- and y-components of the vector are -14.3 cm and 8.8 cm, respectively.