Find the negative value of an angle coterminal with 190 degrees.
We’ll come back to what the word coterminal means in a moment. But first, let’s consider what an angle of 190 degrees looks like in standard position. The initial side of this angle lies along the positive 𝑥-axis. The convention when describing angles on a rectangular coordinate system is that positive angles are measured in a counterclockwise direction from the positive 𝑥-axis, whereas negative angles are measured in a clockwise direction from the positive 𝑥-axis.
The angle we’re interested in is positive 190 degrees, which means it’s 190 degrees in a counterclockwise direction from the positive 𝑥-axis. This angle will be in the third quadrant as an angle of 180 degrees would be on the negative 𝑥-axis and we’re going 10 degrees further.
Now, let’s consider what the question asked us to do. It wants us to find the negative value of an angle coterminal with this angle of 190 degrees. Two angles are described as being coterminal if they have the same initial and terminal sides. This means that we’re looking for a different way of describing the angle that we’ve already drawn.
As we’re looking for a negative value, this means that instead of describing the angle in a counterclockwise direction, we instead describe it in a clockwise direction. Angles around a point sum to 360 degrees, which means we can find the magnitude of this angle by subtracting 190 from 360, giving 170 degrees. We then need to make this value negative so that it describes movement in a clockwise direction.
The negative value which is coterminal with 190 degrees is negative 170 degrees.