SparklyUnicorn Posted March 26, 2015 Share Posted March 26, 2015 Why are there keys for this on a calculator? For years I thought this must be something really complicated and magical that it has keys on a calculator for it. We are going over this now and um..no it's pretty straight forward. I assume it gets more complicated? Right? I'm kinda disappointed. I thought this was mysterious. --- Ok ok...edited to add we have done more since and now I get it. I think I did learn this in school...maybe. It's been so long! Quote Link to comment Share on other sites More sharing options...
regentrude Posted March 26, 2015 Share Posted March 26, 2015 The keys are there so that you can compute the values sine, cosine and tangent function of an angle. The definition of the function through the sides of a right triangle may be straightforward, but these are very nonlinear functions and it is not possible to calculate the sin or cos of any angle easily without the help of a calculator. Students may memorize the values for 30, 45, 90 and 60 degrees, and for some angles you can use addition theorems using these values, but if you need, say, the sine of 23 degrees, calculator is your only chance... unless you do a Taylor series expansion and sum the series which takes forever. How would you calculate sin(23 degrees)? ETA: When I was in school, we had tables for the trig functions. You'd look up the nearest values and interpolate. 9 Quote Link to comment Share on other sites More sharing options...
kiana Posted March 26, 2015 Share Posted March 26, 2015 ??? How are you going to get sine of 1.43 degrees without a calculator or tables? It's easy if it's in a triangle where you know the sides, or of an angle that has a nice answer like 60 degrees, but the calculator will give you values for anything. 2 Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted March 26, 2015 Author Share Posted March 26, 2015 The keys are there so that you can calculate the sine, cosine and tangent function of an angle. The definition of the function through the sides of a right triangle may be straightforward, but these are very nonlinear fuctions and it is not possible to calculate the sin or cos of any angle easily without the help of a calculator. Students may memorize the values for 30, 45, 90 and 60 degrees, but if you need the sine of 23 degrees, calculator is your only change... unless you do a complicated series expansion and sum the series. How would you calculate sin(23 degrees)? Ah ok now this is making more sense to me. We've only covered it so far the other way around. Where we know the lengths of the sides. For when it says to figure out something like sin(23 degrees) it only says to use a calculator. So that would be the complicated part. Well I am still curious how to figure it out by hand. Thank you. Quote Link to comment Share on other sites More sharing options...
deerforest Posted March 26, 2015 Share Posted March 26, 2015 ETA: When I was in school, we had tables for the trig functions. You'd look up the nearest values and interpolate. Wow, thanks for that nearly 30-year flashback! I had completely forgotten about those tables! 3 Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted March 26, 2015 Author Share Posted March 26, 2015 ??? How are you going to get sine of 1.43 degrees without a calculator or tables? It's easy if it's in a triangle where you know the sides, or of an angle that has a nice answer like 60 degrees, but the calculator will give you values for anything. I'm magical that way? LOL Kidding... I'm just learning this stuff. It first explained the easy part! 1 Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted March 26, 2015 Author Share Posted March 26, 2015 We must have had the tables. We never used calculators, but I do recall tables. Quote Link to comment Share on other sites More sharing options...
kiana Posted March 26, 2015 Share Posted March 26, 2015 Before calculators, tables were used -- these (and the calculators) can get their values by using several terms of the Taylor series for sin x, or by using a more complicated algorithm involving complex numbers -- http://www.homeschoolmath.net/teaching/sine_calculator.php 1 Quote Link to comment Share on other sites More sharing options...
regentrude Posted March 26, 2015 Share Posted March 26, 2015 Ah ok now this is making more sense to me. We've only covered it so far the other way around. Where we know the lengths of the sides. For when it says to figure out something like sin(23 degrees) it only says to use a calculator. So that would be the complicated part. Well I am still curious how to figure it out by hand. To do it by hand, you could use a protractor and construct a right triangle with a 23 degree angle, then use a ruler to measure the opposite side and the hypotenuse, and then compute the ratio. Time consuming and inaccurate. Alternatively, you can do a Taylor series expansion (requires calculus) or look it up in a book, which gets you a polynomial with infinitely many terms. For the sine function is is x- x^3/3!+x^5/5!+... you would need to convert the angle into radians. Nobody in their right mind would do this - but that's how the calculator does it internally, I believe. Or you can find a way to express your angle as a sum or difference of angles for which you happen to know the values of sine and cosine and apply trig identities (there are some for sums and differences and double angles and half angles). 1 Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted March 26, 2015 Author Share Posted March 26, 2015 I haven't done any of this since oh 1990. 1 Quote Link to comment Share on other sites More sharing options...
mathmarm Posted March 26, 2015 Share Posted March 26, 2015 Why are there keys for this on a calculator? I wont say how long I've been teaching math, but its been a long time and this is definitely not the dumbest math question ever. I promise you, its not. :) For years I thought this must be something really complicated and magical that it has keys on a calculator for it. We are going over this now and um..no it's pretty straight forward. I assume it gets more complicated? Right? Yes, it gets more complicated. Typically things are introduced in their most straight-forward manner and some basic exercises are given so that you can get the hang of it and familiarize yourself with the most oft-repeated problems and might even memorize the solutions to the really easy things that you need to know (sort of how kids learn the concept and perform the operation of addition/subtraction to get a feel for it, and then learn their facts by heart.) I'm kinda disappointed. I thought this was mysterious. Many people do, its where half of the math phobia and anxiety in students comes from. They fear what they don't know because they find its mystery intimidating. However, these are NOT simple linear functions and the answer won't always be as easy as to find. The calculator is there to save you from having to compute cosine (47.9 deg) by hand. Not sure how you--or your text--is, but older books have tables in the backs of them, and we used to refer to the table and interpolate--its extremely tedious and time consuming to do this by hand. 2 Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted March 26, 2015 Author Share Posted March 26, 2015 Thanks so much mathmarm. I am sure I'll come up with something dumber to ask. The explanation just seemed so simple to me that I thought come on there has to be more! Quote Link to comment Share on other sites More sharing options...
daijobu Posted March 30, 2015 Share Posted March 30, 2015 I was a little shocked to see that AoPS uses SOH CAH TOA...the same mnemonic I used in high school ages ago to learn sin cos tan. I remember when it was first suggested to me in math class as a tool to memorize the trig functions. And I thought it was a funny mnemonic because it's essentially a made up word (sounding vaguely Native American)...how would that help me? But sure enough it did the trick. "Tangent...hm...SOH CAH TOA...opposite over adjacent." But I thought in the 21st century someone would have come up with a new and better mnemonic. Quote Link to comment Share on other sites More sharing options...
kiwik Posted March 30, 2015 Share Posted March 30, 2015 I remember learning that. I thought my brain had turned mush because I couldn't work out what to do. It turned out they were just teaching the definitions for use in the next year. I hate memorising stuff without explanations. Quote Link to comment Share on other sites More sharing options...
AMJ Posted March 30, 2015 Share Posted March 30, 2015 Wow, thanks for that nearly 30-year flashback! I had completely forgotten about those tables! You mean they don't still have the tables? I'm going to have to go to an ANTIQUE bookstore to find the type of text I used in high school? I'm going to have to give my kids MORE evidence that I'm older than the hills? Well, they are already well aware of that. I'll find some old examples, and add them to my ongoing here's-what-we-did-before-wheels-and-phones lecture series. :D Quote Link to comment Share on other sites More sharing options...
AMJ Posted March 30, 2015 Share Posted March 30, 2015 I haven't done any of this since oh 1990. You are such a young kid! 2 Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted March 30, 2015 Author Share Posted March 30, 2015 You are such a young kid! Probably not. Looking at the ages of your kids I might be a similar age. Quote Link to comment Share on other sites More sharing options...
Luckymama Posted March 30, 2015 Share Posted March 30, 2015 I like to pull out trig tables every once in a while to show dd just how easy she has it :lol: 2 Quote Link to comment Share on other sites More sharing options...
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