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
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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.