A vector with magnitude 4 points in a direction 130 degrees counterclockwise from the positive x axis.
so, question ?
To find the vector with magnitude 4 pointing in a direction 130 degrees counterclockwise from the positive x-axis, we can use trigonometry.
First, we convert the angle from degrees to radians, since trigonometric functions in most programming languages require input in radians. To convert from degrees to radians, we use the formula:
angle_in_radians = (angle_in_degrees * π) / 180
In this case, the angle in degrees is 130, so the angle in radians is:
angle_in_radians = (130 * π) / 180
Now, we can use trigonometric functions (sine and cosine) to find the x and y components of the vector.
The x component of the vector can be found using the cosine function:
x = magnitude * cos(angle_in_radians)
Substituting the given values:
x = 4 * cos((130 * π) / 180)
Similarly, the y component of the vector can be found using the sine function:
y = magnitude * sin(angle_in_radians)
Substituting the given values:
y = 4 * sin((130 * π) / 180)
Therefore, the vector with magnitude 4 pointing in a direction 130 degrees counterclockwise from the positive x-axis can be represented as (x, y) where:
x = 4 * cos((130 * π) / 180)
y = 4 * sin((130 * π) / 180)