Transcript:

How to remember trigonometric values of reference angles. I'm Bon Crowder with MathFour.com and we're talking about reference angles and how to remember the trig values for each of those. So, we have three reference angles, 30 degrees, 45 degrees and 60 degrees. And if you consider the triangles made out of each of these reference angles, you might remember that a 30, 60, 90 triangle has the ratios of one, two, square root of three. So, it's one, two, square root of three. And a 30 degree triangle, same as 60 degree right angle. So, it's one, two and square root of three. And a 45, 45, 90 triangle has the ratios of one, one and square root of two. So, if you remember those, then we can go to the sine, cosine and tangent and use a special mnemonic device to remember how to calculate those. I use good, old Oscar. Oscar has a hunk of apple. So, Oscar and of is the opposite angle, I'm sorry, the opposite side from the angle. Has is the hypotenuse and Oscar has a hunk, has and hunk are the hypotenuse. And A which is A and apple, is the adjacent. So, in a triangle, if this is your special angle, there he is, little happy angle. This is the opposite, here's my right angle, it's a little crooked. Here is my adjacent side and here is the hypotenuse. So, up here, the sine of 30 degrees is the opposite over the hypotenuse. The cosine of 30 degrees is the adjacent over the hypotenuse and the tangent of 30 degrees is the opposite over the adjacent. Now, it might be nice to rationalize that denominator, right. So, we have the square root of three over three. Now, go to the 45 degree angle and we have the sine of the 45 degree angle, is opposite over hypotenuse. Probably got to rationalize that denominator. Cosine is the adjacent over the hypotenuse, gee, golly, there's a lot of rationalize and denominators around here. And the tangent is the opposite over the adjacent. One more reference angle to go. the 60 degree angle, the sine of 60 degrees is the opposite over the hypotenuse. The cosine is the adjacent over the hypotenuse and the tangent is the opposite over the adjacent. And there I have all of my trigonometric values for my reference angles. Now, did I memorize them? No, but I don't have to clutter my brain with that. Because I know all of my mnemonic devices and I know my special triangles. I'm Bon Crowder with MathFour.com, this is a lot of fun, isn't it?