04 - What is the Unit Circle? Angle Measure in Degrees, Reference Angles & More.

Finally, we count around the unit circle in increments of degree measure to find the position of any point on the unit circle. This will be used later to solve problems that involve the sine, cosine, and tangent of an angle in standard position. Standard position means that the initial size of the angle is on the positive x-axis and the terminal side of the angle falls somewhere else on the unit circle.

[kennethwoods]

This is a good instructor because he is spending a lot of time providing foundational information about the unit circle before you have to switch over to radian measures. Other instructors immediately begin to layer radian measures on top of the unit circle degrees so you feel a bit overwhelmed. That's especially true if you are still learning what sine, cosine, tangent, etc are. Here, you are being strongly encouraged to take the time to learn where the degrees are before they are replaced by radian measures. I also noticed how he encouraged you to see how each degree can be seen 2 ways depending on if you are going clockwise or counter clockwise. Now, on to the radian measures. He warned you! 👍

[autolancegega]

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[RB]

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Thank you so much

[billiecrisp]

Thank you. Cleared up 70 years of confusion!

[luisfernandolebrando]

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[rehoboth_farm]

I found a really neat way to construct the unit circle when I was in high school. It requires adding 4 additional lines. Just divide the circle into equal 15 degree graduations. Then starting at the 0 degree line and number 0-24 going around counter clockwise ending back at the same line. I call these numbers "Q" Then theta= QPi/12 . This method can actually be used to determine the exact radian measure for any number of even divisions substituting also half the number of divisions for the numerator. If you divide the circle into 360 equal parts then theta=QPi/180. I've never seen anybody else ever do this and I'm more than old enough to have kids in high school. I never had to memorize the values of the unit circle because I knew how to make it. Sure, I get the whole special right triangle thing but I've always believed this was somehow really important. My high school trig teacher just got mad at me. I've never understood why.

[judparn]

Thanks for your patience. Please include in your illustrations the "unreduced" form of the pi fractions. As is, I don't get the numeric progression of the pi fractions from O radian to 2 pi. Or is there?

[monicasalawe]

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[louiseangela]

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[shreyashjoshi]

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[hemarajue]

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[johnlshilling]

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[balaeinstein]

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[acejanea]

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[shimelesbiru]

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