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DO NOW
DO NOW
The labeled angle is 125 degrees. How many degrees is the unlabeled angle? (the one that goes counter-clockwise)
Hint: how many degrees is the whole circle?
Hint: how many degrees is the whole circle?
LEARNING TARGET
LEARNING TARGET
I can find coterminal angles.
I can find coterminal angles.
Studium: I told you we would get telepathic today, but I forgot that today is Mr. Overholt day (Hi Mr. Overholt!) We will get telepathic tomorrow instead. Sorry!
I DO
I DO
what are coterminal angles?
what are coterminal angles?
Two angles that end in the same place on the unit circle. Since they end in the same place, they have the same (x, y), and therefore the value of all the trig functions for two coterminal angles are the same.
Two angles that end in the same place on the unit circle. Since they end in the same place, they have the same (x, y), and therefore the value of all the trig functions for two coterminal angles are the same.
Yeah, well, who cares?
Yeah, well, who cares?
This has come up in our work a few times. For example, if we tried to find sin(420), we noticed that we couldn't do it because the unit circle doesn't go that high. Or, sometimes we get confused when the angle is negative. After today - no more!
This has come up in our work a few times. For example, if we tried to find sin(420), we noticed that we couldn't do it because the unit circle doesn't go that high. Or, sometimes we get confused when the angle is negative. After today - no more!
how do you find these angles?
how do you find these angles?
If I'm standing at a particular spot on the unit circle, I can get back to that same spot just by walking all the way around the circle in either direction (which means I would end up in the same spot, so those would be coterminal angles). Walking all the way around the circle means going 360 degrees. So, you can find a coterminal angle of any angle by adding or subtracting 360 from it.
If I'm standing at a particular spot on the unit circle, I can get back to that same spot just by walking all the way around the circle in either direction (which means I would end up in the same spot, so those would be coterminal angles). Walking all the way around the circle means going 360 degrees. So, you can find a coterminal angle of any angle by adding or subtracting 360 from it.
If the angle is in radians, the "whole circle" is 2π, so you would add or subtract 2π to find a coterminal angle.
If the angle is in radians, the "whole circle" is 2π, so you would add or subtract 2π to find a coterminal angle.
Here is a video you can watch if you want, but you might not need it:
Here is a video you can watch if you want, but you might not need it:
Let's do some examples!
Let's do some examples!
- Find the coterminal angle that is between 0 and 360 degrees: -50°
- Find the coterminal angle that is between 0 and 360 degrees: 950°
- Find the coterminal angle that is between 0 and 2π radians: -2π/3
- Find the coterminal angle that is between 0 and 2π radians: 11π/2
- Find one negative and one positive coterminal angle: π/6
WE DO
WE DO
Let's start our work together. Work on your own when you're ready!
YOU DO
YOU DO
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