The horizontal component of the angle is as large as it can get, but, it's also negative. Consider the central angle itself and the unit circle. The vertical component of the angle is as large as the radius, but it's also negative. The vertical leg is 0, so the sine is 0. Dohyun Certified Tutor. William M. Certified Tutor. Luther College, Bachelor in Arts, Mathematics. Report an issue with this question If you've found an issue with this question, please let us know. Do not fill in this field.
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Top Subjects. Current timeTotal duration Google Classroom Facebook Twitter. Video transcript Voiceover:Let's explore the unit circle a little bit more in depth. Let's just start with some angle theta, and for the sake of this video, we'll assume everything is in radians. This angle right over here, we would call this theta.
Now let's flip this, I guess we could say, the terminal ray of this angle. Let's flip it over the X and Y-axis. Let's just make sure we have labeled our axes. Let's flip it over the positive X-axis.
If you flip it over the positive X-axis, you just go straight down, and then you go the same distance on the other side. You get to that point right over there, and so you would get this ray. You would get this ray that I'm attempting to draw in blue. You would get that ray right over there. Now what is the angle between this ray and the positive X-axis if you start at the positive X-axis? Well, just using our conventions that counterclockwise from the X-axis is a positive angle, this is clockwise.
Instead of going theta above the X-axis, we're going theta below, so we would call this, by our convention, an angle of negative theta. Now let's flip our original green ray. Let's flip it over the positive Y-axis. If you flip it over the positive Y-axis, we're going to go from there all the way to right over there then we can draw ourselves a ray. My best attempt at that is right over there. What would be the measure of this angle right over here?
What was the measure of that angle in radians? We know if we were to go all the way from the positive X-axis to the negative X-axis, that would be pi radians because that's halfway around the circle.
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