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Math Help - Calculator-less Calculus

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    Calculator-less Calculus

    Where I went to high school, we were actually given graphing calculator for trig, alg 2, calc, and prob/stat, but now I'm going into a college level Calculus I class and can't do anything without a calculator (trig functions, ln, log, etc.). While I would still question the need for a full-on ban of calculators, I still see this as a major shortcoming and would like to try to work on it before our test on pre-calculus . Can anyone explain to me how to do this?

    (I should also probably add that I understand the concepts of the functions since I've had to use them before, I just can't use them without a calculatoR).
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    Quote Originally Posted by davesface View Post
    Where I went to high school, we were actually given graphing calculator for trig, alg 2, calc, and prob/stat, but now I'm going into a college level Calculus I class and can't do anything without a calculator (trig functions, ln, log, etc.). While I would still question the need for a full-on ban of calculators, I still see this as a major shortcoming and would like to try to work on it before our test on pre-calculus . Can anyone explain to me how to do this?

    (I should also probably add that I understand the concepts of the functions since I've had to use them before, I just can't use them without a calculatoR).
    not having a calculator means you are going to have to use a bit more memory. as far as what you are asking is concerned, you are being way too vague. it is best that you be specific about what kinds of problems you are needing help with at the moment. deal with one topic at a time, to go through all that you asked in one shot is too much work
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    I probably most need to know how it is possible to evaluate something like sin(37) or any other trig function on any abnormal value (not 0, 30, 45, 60, or 90). Any resource would be helpful, even if you can't show me some of these things.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by davesface View Post
    I probably most need to know how it is possible to evaluate something like sin(37) or any other trig function on any abnormal value (not 0, 30, 45, 60, or 90). Any resource would be helpful, even if you can't show me some of these things.
    you cannot find the value of something like sin(37). if you are not allowed to use calculators, then you would be expected to leave sin(37) as is in your answer. what you could be expected to find exactly though are things like \sin(105^o) or \cos \frac {7 \pi}6. for these you need to review two topics: (trig values of) special angles and reference angles. you should take some time to review these topics and come back with questions, because it itself is also a fairly large topic, sort of.

    you can search for threads here as well. many problems like these have been done on this forum. try searching for evaluating/simplifying trig functions here and, of course, on google

    i really think you should come back with specific problems, explaining these things right off the bat will be difficult, and re-inventing the wheel
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    So is it basically just the use of various trig identities combined with the basic angles' values?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by davesface View Post
    So is it basically just the use of various trig identities combined with the basic angles' values?
    yes. and reference angles. you also need to know the quadrants for which each trig value is negative or positive. for instance, you should know that sine gives positive values in the first and second quadrant, but negative values in the third and fourth. and of course, you should know what we mean by "quadrant"
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    Quote Originally Posted by Jhevon View Post
    you cannot find the value of something like sin(37). if you are not allowed to use calculators, then you would be expected to leave sin(37) as is in your answer.
    Once you get into Calculus I, you'll learn something called Linear Approximation, which will allow you to evaluate things like sin(37) without a calculator. In the meantime though, leave such answers as sin(37).
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  8. #8
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    Quote Originally Posted by davesface View Post
    I probably most need to know how it is possible to evaluate something like sin(37) or any other trig function on any abnormal value (not 0, 30, 45, 60, or 90). Any resource would be helpful, even if you can't show me some of these things.
    In the old days (BC), you had a set of trig tables in which you interpolated data in order to construct new data points within the range of a discrete set of known data points. You can find such a table here: Trigonometric Tables

    But, I can't imagine going back to that method.
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    Quote Originally Posted by mathgeek777 View Post
    Once you get into Calculus I, you'll learn something called Linear Approximation, which will allow you to evaluate things like sin(37) without a calculator. In the meantime though, leave such answers as sin(37).
    I've already taken Calculus (albeit a year and a half ago, darn block scheduling!) and remember linear approximation, but I'm looking for more pre-calculus style things. I just found out today that specifically we need to be able to do the type of problems found here.

    1 specific example problem would be:

    The value of sin (x) is 1/5 . Express the value of csc (x) as an integer.
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  10. #10
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    That does not require any use of a calculator but the knowledge of the fact that: \csc x = \frac{1}{\sin x}

    Now it is just a matter of plugging in: \csc x = \frac{1}{{\color{blue}\sin x}} = \frac{1}{{\color{blue}\frac{1}{5}}} = 5

    No need to find out what x actually is,
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    Yeah, I realized shortly after posting it that that problem was perhaps the worst possible one to randomly pick. Here is another one:

    The value of sin (x) is 1/5. The value of cos^2 (x) can be written in the form 6a^2. Express the value of a^2 in simplest form (as an irreducible quotient of two integers).
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  12. #12
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    this is just an exercise in knowing how to use the Pythagorean identity \cos^2{x} + \sin^2{x} = 1

    you were given ...

    6a^2 = \cos^2{x}

    and

    \sin{x}=\frac{1}{5}

    manipulating the Pythagorean identity ...

    \cos^2{x} = 1 - \sin^2{x}

    you should now be able to determine a^2.
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