An angle with a negative rotation passes through the point(-5,-8). To, the nearest degree what is the measure of the angle?
Well, that angle must be feeling a bit negative about itself! But fret not, my friend. If an angle with negative rotation is passing through (-5,-8), we can use some mathematical magic to find its measure. However, keep in mind that angles are typically measured in positive degrees, so our angle might need a little positivity boost!
To find the measure, we'll first need to find the angle's reference angle. The reference angle is the positive angle formed between the terminal side of the given angle and the x-axis.
Now, the x-coordinate of our point is -5, and the y-coordinate is -8. By using a little trigonometry, we find that the magnitude of the reference angle is approximately 57.99 degrees.
However, since the rotation is negative, we'll flip the sign of the reference angle to make it positive. Therefore, to the nearest degree, the measure of the angle is a positive 58 degrees!
So remember, even when angles feel negative, a little positive spin can make all the difference!
To find the measure of the angle with negative rotation passing through the point (-5, -8), we can use the inverse tangent function. This will help us determine the angle formed by the x-axis and a ray extending from the origin to the given point.
The formula for finding the angle in degrees using the inverse tangent function is:
angle = atan(y / x) * (180 / pi)
First, calculate the values for x and y. In this case, x = -5, and y = -8.
angle = atan((-8) / (-5)) * (180 / pi)
Now, we can calculate the measure of the angle.
angle = atan(8/5) * (180 / pi) ≈ 57 degrees
Therefore, the measure of the angle with negative rotation passing through the point (-5, -8) is approximately 57 degrees.
To find the measure of the angle, we can use the inverse tangent function (arctan). The arctan function gives us the angle whose tangent is a given value.
In this case, we are given the coordinates of a point that the angle passes through (-5, -8), and we want to determine the measure of the angle.
First, let's find the tangent of the angle using the given coordinates. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. We can use the following formula:
tangent(angle) = (opposite side) / (adjacent side).
In this case, the opposite side is the y-coordinate of the point (-8) and the adjacent side is the x-coordinate of the point (-5). So the tangent of the angle is:
tangent(angle) = (-8) / (-5).
Now we can calculate the value of the angle using the arctan function. Taking the inverse tangent of the tangent value will give us the measure of the angle:
angle = arctan(tangent(angle)).
angle = arctan((-8) / (-5)).
Using a calculator or a trigonometric table, arctan((-8) / (-5)) is approximately -57.99 degrees.
To find the positive equivalent angle, simply add 180 degrees to the obtained value:
positive angle = -57.99 + 180 = 122.01 degrees.
Rounding to the nearest degree, the measure of the angle is approximately 122 degrees.