What is the angle (in standard position - i.e. measured counterclockwise from the positive x-axis) formed by a line from the origin to point (1,-2)?

Please help and Thank you

post.

To find the angle formed by a line from the origin to point (1, -2), you can use trigonometry. Let's label the x-coordinate as x and the y-coordinate as y.

The formula to find the angle in standard position is:

θ = atan(y / x)

Where atan represents the inverse tangent function.

In this case, x = 1 and y = -2. Substituting these values into the formula, we get:

θ = atan((-2) / 1)

Using a calculator, we can find the angle:

θ ≈ -63.4 degrees

So the angle in standard position formed by the line from the origin to point (1, -2) is approximately -63.4 degrees.

To find the angle in standard position formed by the line from the origin to the point (1, -2), you can use trigonometry.

1. Begin by observing that the line from the origin to the point (1, -2) forms a right-angled triangle with the x-axis.
2. The x-coordinate of the point (1, -2) is 1, and the y-coordinate is -2.
3. Calculate the length of the hypotenuse of the triangle by using the Pythagorean theorem: hypotenuse = sqrt(x^2 + y^2) = sqrt(1^2 + (-2)^2) = sqrt(1 + 4) = sqrt(5).
4. Next, determine the value of the angle formed by the line with the x-axis by using the inverse trigonometric function. In this case, we will use the arctan function (also known as the inverse tangent).
- You can calculate this angle as follows: angle = arctan(y / x) = arctan(-2 / 1) = arctan(-2) ≈ -63.43°.
- Since the angle is measured counterclockwise from the positive x-axis, a negative value means rotating clockwise. Therefore, the angle is actually 360° - 63.43° = 296.57°.

Hence, the angle formed by the line from the origin to the point (1, -2) in standard position is approximately 296.57 degrees (or radians, if preferred).

tanAr = Y/X = -2/1 = -2.

Ar = -63.43 Deg., CW. Q4.
A = -63.43 + 360 = 297 Deg., CCW.