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
To find the angle formed by a line from the origin to a given point in standard position, you can use the inverse tangent function.
First, calculate the tangent of the angle. In this case, the point is (1, -2), which means the x-coordinate is 1 and the y-coordinate is -2.
Next, divide the y-coordinate by the x-coordinate to get the tangent of the angle:
tan θ = -2/1 = -2
Now, take the inverse tangent (also called arctangent) of -2 to find the angle:
θ = arctan(-2)
Using a scientific calculator or an online calculator with trigonometric functions, calculate the arctan(-2). The result is approximately -63.43 degrees.
Since the angle is measured counterclockwise from the positive x-axis in standard position, we know that the angle formed is 180 degrees minus the calculated angle.
So, the angle formed by the line from the origin to point (1, -2) is:
180 - 63.43 ≈ 116.57 degrees
Therefore, the angle is approximately 116.57 degrees.