❤︎² How to Remember the Unit Circle (mathbff)
Trki, Kody, Cheaty do
MIT grad shows how to remember the unit circle angles and points. More videos with Nancy coming in 2017! The unit circle is a circle of radius one. For each angle, there is a point on the circle whose x-coordinate is the cosine value of the angle and whose y-coordinate is the sine value of the angle. There are patterns within the unit circle that make it easier to understand and to memorize. ANGLES (in radians): First, the radian angle measures of the four "corner" points on the circle are 0, pi/2, pi, 3pi/2, and 2pi. The 2pi angle is one complete full circle around the unit circle and is in the same position as the 0 angle measure. Next, it's easiest to identify the "pi/4" angles, as they are each in the exact middle of a quadrant. Pi/4 can be marked in the middle of the first quadrant (Quadrant I), 3pi/4 is in the middle of the second quadrant, 5pi/4 is in the middle of the third quadrant, and 7pi/4 is in the middle of the fourth quadrant. Next, the "pi/6" angles are positioned closer to the x-axis and are pi/6, 5pi/6, 7pi/6, and 11pi/6. Finally, the "pi/3" angels are positioned closer to the y-axis and are pi/3, 2pi/3, 4pi/3, and 5pi/3. (X,Y) POINT FOR EACH ANGLE GIVES YOU SIN AND COS: There are patterns to remember the (x,y) coordinates of the point on the circle that corresponds to each angle mentioned above. Since each of the four "corner" points at 0, pi/2, 3pi/2, and 2pi is a distance of one full unit from the origin center of the circle, their coordinates are each (1,0), (0,1), (-1,0), and (0, -1), respectively. NOTE: For the other angles, you only need to remember these three important numbers: 1/2 (square-root of 2)/2 (square-root of 3)/2 You just need to remember that: 1) The SMALLEST of these numbers is 1/2 2) The MID-SIZED number is (square-root of 2)/2 3) The LARGEST of these numbers is (square-root of 3)/2 For each of the remaining angles (for instance pi/6, pi/4, pi/3, etc), if the corresponding point on the circle has the smallest possible x-distance, its x-coordinate is 1/2, and if it has the largest possible x-distance, its x-coordinate is (square-root of 3)/2. If it has the middle distance, its coordinate value is (square-root of 2)/2. The same is true for the y-values. NOTE: Remember that the x-coordinate is the cos value, and the y-coordinate will give you the sin value.
Komentarze
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My teachers are never as good as people online. Just memorized this in about 10 minutes when that would never happen trying to do it by myself
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Very helpful video! Thank you
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süpersin hayatım
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What if you have to find points not directly identified by the unit circle and you have to find their sin,cos & tan. that's where i get confused. for example 8pi/7
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Should have worn a white outfit. I cant see the writing !!!!
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blue screen
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I wonder why her videos get so much more attention than other math videos on youtube... HMMMMMMM......
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You do a great job with these videos.your videos help me a lot. Anyone serious about learning math should look them up.Thank you so much!
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Thank you so much I really appreciate it
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Brilliant. Love this.
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When my workstation screen was at a 90 degree angle. My lips intersected yours at the X and Y axis, but were also tangent to yours, on the Z axis. Basically, I kissed my screen lol:)
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u r beautiful dear teacher
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does this video delivers what it says? HELL NO
she just made a unit circle and put the values in front of you to mock you that she does remembers this -
How did you get 5pi/6, because when i added pi/6 with pi/2 i got 4pi/6 ??? i seriously need help with this
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thanks gros bissouuuuuuuuuuuuu
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Very helpful, thanks
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Are you writing with your right hand? Or writing backwards with your left hand? Now that is the question.
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At first i used to only concentrate on you but in this video i managed to do both..lol..i learnt it and now i love you even more. i would love some personal tutoring..(in bed)