Find the component form for vector v with the given amplitude and direction angle theta.
|v|=20.6, theta=102.5deg
(x,y) = (20.6cos102.5° , 20.6sin 102.5°)
To find the component form of a vector given its amplitude and direction angle, we can use trigonometry.
Let's assume that the vector v has components (x, y). The amplitude of the vector is denoted by |v|, which represents the magnitude of the vector. In this case, |v| = 20.6.
The direction angle theta is the angle between the positive x-axis and the vector v. In this case, theta = 102.5 degrees.
To find the components x and y, we can use the following trigonometric relationships:
x = |v| * cos(theta)
y = |v| * sin(theta)
Let's substitute the given values into these equations:
x = 20.6 * cos(102.5)
y = 20.6 * sin(102.5)
Calculating these values will give us the component form of the vector v.