SOLUTION: The terminal arm of an angle in standard position passes through the point (4, -3). a) Find the radian value of the angle in the interval [0,2𝜋].

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Question 1183281: The terminal arm of an angle in standard position passes through the point
(4, -3).
a) Find the radian value of the angle in the interval [0,2𝜋].
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
set yoour calculator to radians.
the opposite side of the angle is equal to -3.
the adjacent side of the angle is equal to 4.
to find the reference angle, use only positive values to get:
tan(x) = 3/4
solve for x to get:
x = arctan(3/4) = .6435011088 radians.
if you draw the angle in the standard position, it will be in the fourth quadrant.
the tangent in the fourth quadrant is negative.
the tangent is also negative in the second quadrant.
the equivalent angle in the second quadrant is pi - .6435011088 = 2.498091545 radians.
the equivalent angle in the fourth quadrant is 2pi - .6435011088 = 5.639684198 radians.
here is the drawing of the angle in the standard position based on the coordinates of (4,-3).

here is the graph of the equation of y = tan(x) and y = -3/4.
the intersection of those two equations give you the solution.
that solution includes the angle in the fourth quadrant and in the second quadrant.

the coordinate points are in (x,y) format.
x is the angle in radians.
y is value of the tangent function which is -3/4 = -.75

the x-values have been rounded to 3 decimal places.