Calculate the angle θ between the radiusvector of the point and the positive x axis (measured counterclockwise from the positive x axis, within the limits of −180◦ to +180◦). Answer in units of ◦.
Calculate the angle θ between the radiusvector of the point and the positive x axis
(measured counterclockwise from the positive
x axis, within the limits of −180◦
to +180◦
).
Answer in units of ◦
.
To calculate the angle θ between the radius vector of the point and the positive x-axis, measured counterclockwise from the positive x-axis, you need to know the coordinates of the point.
Let's assume the coordinates of the point are (x, y). We can use trigonometry to find the angle θ.
First, we calculate the angle in radians using the arctan function: θ = arctan(y / x).
Next, we convert the angle from radians to degrees by multiplying the angle in radians by 180/π.
However, we need to consider the quadrant in which the point lies to determine the correct angle within the range of -180° to +180°.
If the point lies in the 1st or 4th quadrant (where x is positive), we use the calculated value as the angle θ.
If the point lies in the 2nd or 3rd quadrant (where x is negative), we add or subtract 180° from the calculated value, respectively.
So, now you have the step-by-step process to calculate the angle θ between the radius vector of the point and the positive x-axis.