in this video i'm going to give you a simple way to remember trigonometry values but first let's make a table with the values that you need to know and so here we're going to put the sine values and then the cosine values followed by the tangent values and here will be the angles 0 degrees 30 which is pi over 6 45 that's pi over 4 60 is pi over three and ninety which is pi over two so sine of zero is zero sine thirty is one over two or you could say square root one over two sine 45 is square root 2 over 2. sine 60 is square root 3 over 2 and sine 90 is square root 4 over 2. square root 4 is 2 2 divided by 2 is 1. but notice the pattern so i'm going to replace this with a 1. and here i'm just going to take off the square root symbol now cosine is basically the reverse of sine cosine 0 is 1 and we're going to have the same values but going in the other direction cosine 30 is the square root of 3 over 2 cosine 45 root 2 over 2 cosine 60 is one half and cosine 90 is zero now tangent is sine divided by cosine so zero divided by one is zero that's tangent of zero degrees is zero now if we take one half and divided by the square root of three over two the twos will cancel and so it becomes one divided by the square root of three and if you rationalize it if you multiply 1 over square root 3 by root 3 over root 3 this will simplify to the square root of 3 over 3. now tan 45 is going to be sine over cosine because those two values are the same it's going to be one now tangent 60 square root 3 over 2 divided by one half just like before and the twos will cancel and so it's the square root of three divided by one which will simplify to the square root of three and tan 90 is going to be one divided by zero whenever you divide a constant by zero it's undefined so i'm just gonna mark that off so tan 90 is undefined keep that in mind now is there a way in which we can remember basically the values here and it turns out that you could use a special reference triangle to get any one of those values for 30 45 and 60. i'm going to show you how to do it now let's start with the 30 60 90 right triangle across the 30 degree angle the length of the side is going to be a 1. across the 90 degree angle it's a 2 and across the 60 degree angle it's the square root of 3. now you need to be familiar with something called sohcahtoa and let's say if we wish to evaluate sine of 30 degrees so we need to use the so part in sokatoa which tells us that sine is equal to the opposite side divided by the hypotenuse so o stands for opposite h stands for hypotenuse and a represents adjacent so let's focus on the 30 degree angle opposite to the 30 degree angle is 1 and the hypotenuse is the longest side it's across the right angle so the hypotenuse is two the sine thirty is one over two now let's say if we wish to evaluate cosine thirty so we need to use this portion of socotropa so cosine 30 is equal to the adjacent side which is the square root of 3 divided by the hypotenuse which is 2. and so that's how we get this answer root 3 over 2. now let's say if we wish to evaluate tangent of 30 so we would use the toa part of sokatoa so tangent of 30 is equal to the opposite side which is one divided by the adjacent side which is root three and of course we need to rationalize it the square root of three times the square root of three three times three is nine and the square root of nine is three so this becomes root three over three and so that's how we can evaluate tangent 30 using the excuse me the 30 60 90 the right triangle now if we wish to evaluate tangent of 60 we would focus on this angle opposite to the 60 degree angle is the square root of three and adjacent to it is one so it's the square root of three divided by one which is simply square root three and let's do one more with this triangle so let's say if we wish to evaluate sine of 16. so using the so part of sohcahtoa we know that sine 60 is equal to the opposite side divided by the hypotenuse and so that becomes the square root of three over two and so that's a simple trick in which you can remember the trigonometry values you could use that to evaluate the common trigonometry functions now let's use the 45 45 right triangle this is the other one that you need to know now across the 45 degree angles the side lengths will be the square root of two actually no i take that back it's going to be one they have to be the same though but across the hypotenuse is the square root of two so let's say if we wish to evaluate sine of 45 degrees so we could use any one of the two 45 degree angles so it's going to be the opposite side divided by the hypotenuse based on sohcahtoa so opposite to 45 is 1 and the hypotenuse is the square root of 2. now anytime you have a a square root symbol in the bottom of a fraction you need to rationalize it so let's multiply the top and the bottom by the square root of two so this becomes the square root of two and two times two is four and the square root of four is two so therefore sine 45 can be simplified to root two over 2 and the same is true for cosine 45. now if we wish to calculate tangent of 45 we would still use the same reference triangle based on the torah part of sohcahtoa tangent is opposite divided by the adjacent side so the tangent ratio for a 45 degree angle will be one over one which is simply one and so that's how you could use the 45 45 90 degree triangle to evaluate things like sine 45 tangent 45 or even cosine 45. now let's try another example let's work on secant of 60 degrees feel free to try that problem how can we evaluate secant of 60 now it's important to know that secant is the reciprocal function of cosine so secant 60 is 1 over cosine 60. now we know what cosine 60 degrees is using a table or using the 30 60 90 reference triangle we know that cosine 60 is one half so what's one divided by a half well we can multiply the top and bottom by two one times two is two and one half times two is one the twos will cancel and so secant of sixty is two now what about cosecant of 60 try that one cosecant is the reciprocal of sine and sine 60 is the square root of 3 over 2. so let's multiply the top and the bottom by two so the twos will cancel and what we have left over is two divided by the square root of three now we need to multiply the top and the bottom by the square root of three and so 3 times 3 is 9 and the square root of 9 is 3. so cosecant of 60 is 2 square root 3 over 3. now let's try a problem with tangent let's evaluate tangent of let's say 60 degrees i mean not tangent let's take that back cotangent of 60 degrees cotangent is the reciprocal of tangent so cotangent is 1 over tangent and we know that tangent of 60 is the square root of 3. so we need to rationalize this one let's multiply the top and the bottom by the square root of 3 and so we get root 3 over root 9 and the square root of 9 is 3. so cotan of 60 is root 3 over 3 and that's basically it for this video now for those of you who 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