A vector has a magnitude of 18.2 cm and makes an angle of 129.0° with the positive x-axis. What are the x- and y-components of this vector

x: 18.2 cos 129 = -18.2 cos51

= -11.45 cm
y: 18.2 sin 129 = 18.2 sin51
= 14.14 cm

To find the x- and y-components of the vector, we can use trigonometry.

The x-component of the vector can be found by taking the magnitude of the vector and multiplying it by the cosine of the angle with the positive x-axis.

x-component = magnitude * cos(angle)

In this case, the magnitude of the vector is given as 18.2 cm and the angle is given as 129.0°.

x-component = 18.2 cm * cos(129.0°)

Using a scientific calculator, evaluate the cosine of 129.0°, which is approximately -0.575 (rounded to three decimal places).

x-component ≈ 18.2 cm * (-0.575)

The x-component of the vector is approximately -10.485 cm (rounded to three decimal places).

Now, let's find the y-component of the vector. The y-component can be found by taking the magnitude of the vector and multiplying it by the sine of the angle with the positive x-axis.

y-component = magnitude * sin(angle)

Using the same values as above:

y-component = 18.2 cm * sin(129.0°)

Evaluate the sine of 129.0°, which is approximately 0.818 (rounded to three decimal places).

y-component ≈ 18.2 cm * 0.818

The y-component of the vector is approximately 14.883 cm (rounded to three decimal places).

So, the x-component of the vector is approximately -10.485 cm and the y-component is approximately 14.883 cm.