Find the angle (Θ) for a terminal arm with the following coordinates(round to one decimal place):
(5,8)
tan T = 5/8
T = tan^-1 (5/8)
= 32.0 degrees
C(0,0), (5,8).
tanA = (8-0) / (5-0) = 1.6.
A = 58 deg.
Henry is correct
To find the angle (Θ) for a terminal arm with the given coordinates (5,8), you can use inverse trigonometric functions. First, you need to determine the quadrant in which the point (5,8) lies on the Cartesian plane.
Since the x-coordinate is positive (5), and the y-coordinate is positive (8), the point (5,8) is in the first quadrant.
In the first quadrant, the angle (Θ) between the positive x-axis and the terminal arm can be found using the tangent function:
tan(Θ) = opposite/adjacent
In this case, let's say opposite = 8 and adjacent = 5:
tan(Θ) = 8/5
To find the angle (Θ), you can use the inverse tangent (arctan) function:
Θ = arctan(8/5)
Using a calculator, you can calculate the inverse tangent:
Θ ≈ 57.99°
Therefore, the angle (Θ) for a terminal arm with the coordinates (5,8) is approximately 57.99°, rounded to one decimal place.