A line extends from the origin to the point (-2,5). What is the angle in radians, relative to the positive x-axis?
tanθ = y/x = 5/-2
since y>0 and x<0, it will be in QII
Thank you
To find the angle in radians, we can use the arctan function. The arctan, also known as the inverse tangent, gives us the angle whose tangent is equal to a given value. In this case, we can use the x and y coordinates of the given point to calculate the tangent.
The tangent of an angle is given by the formula:
tan(angle) = y / x
In this case, we have the coordinates (-2,5), which means x = -2 and y = 5. Substituting these values into the formula, we get:
tan(angle) = 5 / -2
Using a calculator, we can find the arctan of this value:
angle = arctan(5 / -2)
Calculating this, we get:
angle ≈ -1.19029 radians
Therefore, the angle in radians, relative to the positive x-axis, is approximately -1.19029 radians.
To find the angle in radians relative to the positive x-axis, we can use the concept of inverse trigonometric functions and the coordinates of the point (-2,5).
1. First, let's calculate the slope of the line passing through the origin (0,0) and the point (-2,5). The slope, m, can be found using the formula:
m = (y2 - y1) / (x2 - x1)
= (5 - 0) / (-2 - 0)
= 5 / -2
= -5/2
Note: The slope is negative because as we move from the origin to the given point along the x-axis, the y-coordinate increases.
2. Now, we need to determine the angle θ in radians. Recall that the tangent of an angle is equal to the slope:
tan(θ) = m
Therefore,
tan(θ) = -5/2
3. To find the value of θ, we can take the inverse tangent (also known as arctangent) of both sides:
θ = arctan(-5/2)
Using a calculator, calculate the arctan(-5/2) to find the angle in radians. The result is approximately -1.1909 radians.
Note: The negative value indicates that the angle is measured clockwise from the positive x-axis.
Therefore, the angle in radians, relative to the positive x-axis, is approximately -1.1909 radians.