Question

if we have a point at (5,3) and we rotate this point about the origin by -30 degrees with respect to the x axis. what is it's new location?

Answer 1

To rotate a point about the origin by a certain angle, you can use the formulas x' = x * cos(angle) - y * sin(angle) and y' = x * sin(angle) + y * cos(angle). Substituting the given values into these formulas, we can find the new location of the point.

Step-by-step explanation:

To rotate a point about the origin, you can use the following formulas:

x' = x * cos(angle) - y * sin(angle)

y' = x * sin(angle) + y * cos(angle)

In this case, the point is (5,3) and the angle of rotation is -30 degrees with respect to the x axis. Substituting these values into the formulas gives:

x' = 5 * cos(-30) - 3 * sin(-30)

y' = 5 * sin(-30) + 3 * cos(-30)

Using a calculator to evaluate the trigonometric functions and rounding to 2 decimal places, we get the new location as approximately (-1.87, 5.96).