The point (-4, 3) lies on the terminal side of an angle. What is the angle?

If you mean the angle counterclockwise from the x axis

tan theta = -3/4 in quadrant 2
tan^-1 (.75) = 37
so
theta = 180 - 37 = 143

To find the angle, we can use the inverse tangent function. The formula to find the angle given the coordinates on the terminal side is:

angle = atan(y/x)

So, substituting the coordinates (-4, 3) into the formula, we have:

angle = atan(3/(-4))

Now let's calculate the angle.

To find the angle, we can use the concept of trigonometry.

Step 1: Identify the reference angle.
The reference angle is the positive acute angle between the terminal side of the angle and the x-axis. To find the reference angle, we can calculate the angle formed between the point (-4, 3) and the positive x-axis.

Step 2: Calculate the reference angle.
We can use the tangent function to find the reference angle. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, we can use the coordinates of the point (-4, 3), where -4 represents the adjacent side and 3 represents the opposite side.

tan(theta) = opposite/adjacent
tan(theta) = 3/(-4)

Now we can solve for theta:
theta = arctan(3/(-4))

Using a calculator or a trigonometric table, we find that the arctan(3/(-4)) is approximately -36.87 degrees.

Step 3: Determine the angle.
Since the given point lies on the terminal side of an angle, the angle itself goes beyond 180 degrees. We need to determine the actual angle.

The original angle can be obtained by adding 180 degrees to the reference angle. Using the given reference angle of -36.87 degrees, adding 180 degrees gives us:

theta = -36.87 + 180
theta = 143.13 degrees

Therefore, the angle is approximately 143.13 degrees.