My Math Forum Easy ways to remember sin and cos functions of unit circle?

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 February 2nd, 2012, 07:13 PM #1 Newbie   Joined: Feb 2012 Posts: 1 Thanks: 0 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!
 February 2nd, 2012, 07:42 PM #2 Senior Member   Joined: Jan 2012 Posts: 131 Thanks: 0 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 02:36 PM.
 February 2nd, 2012, 07:45 PM #3 Global Moderator     Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4 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 02:40 PM.
 October 23rd, 2017, 05:47 AM #4 Newbie   Joined: Oct 2017 From: Texas Posts: 6 Thanks: 0 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/
October 23rd, 2017, 05:54 AM   #5
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 Originally Posted by The Chaz 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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