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February 2nd, 2012, 08:13 PM   #1
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Easy ways to remember sin and cos functions of unit circle?

I have a quiz tomorrow in trigonometry, and basically you have to fill out all the sin and cosine functions of the unit circle in 5 minutes...Are there any easy ways or tricks to memorize them fast?

The quiz we took (Every kid failed in the class so we get to retake it): http://i1165.photobucket.com/albums/q59 ... /quiz2.jpg

As you can see i figured out most of all the values but then i ran out of time...the one things that i can't figure out is if its negative or not (well i can figure it out, but it takes to long)...any trick to that? THANKS!
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February 2nd, 2012, 08:42 PM   #2
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Re: Easy ways to remember sin and cos functions of unit circ


Taken from http://tutorial.math.lamar.edu/pdf/AlgebraTrig.pdf

There are 5 "basic" angles, 0, Pi/6, Pi/4, Pi/3, Pi/2.
The sign of trig function depends on the location, call quadrant, follow the rule CAST. (cos, all, sine, tangent)
Example, all cos function in 1st quadrant((3/2)pi to 0pi) are positive; likewise, all tangents in 3rd quadrant are positive, the rest are negative.

Last edited by skipjack; October 23rd, 2017 at 03:36 PM.
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February 2nd, 2012, 08:45 PM   #3
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Re: Easy ways to remember sin and cos functions of unit circ

Easy:

There are 5 values (+/-) on the unit circle. From LEAST TO GREATEST, they are:
0, 1/2, 1/?(2), ?(3)/2, 1

The ZERO AND ONE always go together (i.e if the cosine is zero, then the sine is +/- 1).
The 1/2 and √(3)/2 always go together
The 1/√(2) is always paired with 1/√(2)

cos(theta) = x
sine(theta) = y

x, y are both positive in quadrant I, both negative in quadrant III, and you should know the other two.

So if asked to fill out a unit circle, I would go from left to right, filling in the x-values
(-1, ....) there is just one such point, all the way to the left.
(-√(3)/2, .....) this would be for two points...
(-1/√(2), .....)
(-1/2, ....)
(0, ....)
(1/2, ....)
(1/√(2), ....)
(√(3)/2, ....)
(1, 0) there is just one of this point, too.

Then do the same from top to bottom. It's a little hard to describe via text, but you could knock this sucker out in 30 seconds if you just knew how to move from negative to positive of both x, y axis, and the order of these values from largest to smallest.

But don't take it from me - I only had the unit circle as the groom's cake at my wedding!!!

Last edited by skipjack; October 23rd, 2017 at 03:40 PM.
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October 23rd, 2017, 06:47 AM   #4
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Hey

You can learn basic values of sin, cos, tan at angles 0, 30, 45 degrees.

To memorise them, visit https://www.teachoo.com/5225/955/Wha...---Evaluating/
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October 23rd, 2017, 06:54 AM   #5
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Originally Posted by The Chaz View Post



But don't take it from me - I only had the unit circle as the groom's cake at my wedding!!!
I know this is old. But..
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