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Thread: Trigonometry and calculus

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    Master Sorcerer LilDreamers's Avatar
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    Default Trigonometry and calculus

    I am studying both of them, help me please -A 8th grader from Finland
    Ask me about anything :3 I try to help you!

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    Master Sorcerer LilDreamers's Avatar
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    bump
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    Lesser Wizard iFluffy's Avatar
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    SOH CAH TOA

    SIN - OPPOSITE/HYPOTENUSE

    COSINE - ADJACENT/HYPOTENUSE

    TANGENT - OPPOSITE/ADJACENT

    Also jesus christ I'm a junior in highschool (11th grade) and I just started trigonometry.
    Good luck :<
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    Master Sorcerer DynPlaysGT's Avatar
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    Quote Originally Posted by iFluffy View Post
    SOH CAH TOA

    SIN - OPPOSITE/HYPOTENUSE

    COSINE - ADJACENT/HYPOTENUSE

    TANGENT - OPPOSITE/ADJACENT

    Also jesus christ I'm a junior in highschool (11th grade) and I just started trigonometry.
    Good luck :<
    lol, my maths teacher gave us a better acronym:

    SIN = O/H (Oh Heck)
    COS = A/H (Another Hour)
    TAN = O/A (Of Algebra)

    Not kidding, my actual maths teacher told us this.
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    Master Sorcerer Colmar's Avatar
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    These will help in your study

    sin ( 90- α) = cos α
    cos ( 90- α) = sin α
    tan ( 90- α) = cotan α

    sin ( 90+ α) = cos α
    cos ( 90+ α) = – sin α
    tan ( 90+ α) = – cotan α

    sin ( 180- α) = sin α
    cos ( 180- α) = – cos α
    tan ( 180- α) = – tan α

    sin ( 180+ α) = – sin α
    cos ( 180+ α) = – cos α
    tan ( 180+ α) = tan α

    sin ( 270- α) = – cos α
    cos ( 270- α) = – sin α
    tan ( 270- α) = cot α

    sin ( 270+ α) = – cos α
    cos ( 270+ α) = sin α
    tan ( 270+ α) = – cotan α

    sin ( 360- α) = – sin α
    cos ( 360- α) = cos α
    tan ( 360- α) = – tan α

    sin ( 360+ α) = sin α
    cos ( 360+ α) = cos α
    tan ( 360+ α) = tan α

    For example,
    Sin 300 = Sin 270+30 = -cos 30 = -½√3
    Though it SOMETIMES easier to memorize the table lol
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    Master Sorcerer Selim149's Avatar
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    Quote Originally Posted by Colmar View Post
    These will help in your study

    sin ( 90- α) = cos α
    cos ( 90- α) = sin α
    tan ( 90- α) = cotan α

    sin ( 90+ α) = cos α
    cos ( 90+ α) = – sin α
    tan ( 90+ α) = – cotan α

    sin ( 180- α) = sin α
    cos ( 180- α) = – cos α
    tan ( 180- α) = – tan α

    sin ( 180+ α) = – sin α
    cos ( 180+ α) = – cos α
    tan ( 180+ α) = tan α

    sin ( 270- α) = – cos α
    cos ( 270- α) = – sin α
    tan ( 270- α) = cot α

    sin ( 270+ α) = – cos α
    cos ( 270+ α) = sin α
    tan ( 270+ α) = – cotan α

    sin ( 360- α) = – sin α
    cos ( 360- α) = cos α
    tan ( 360- α) = – tan α

    sin ( 360+ α) = sin α
    cos ( 360+ α) = cos α
    tan ( 360+ α) = tan α

    For example,
    Sin 300 = Sin 270+30 = -cos 30 = -½√3
    Though it SOMETIMES easier to memorize the table lol
    no it will not help, im literally crying rn lmao
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    Master Sorcerer Ohlid's Avatar
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    Trigonometry is so much memorization with the identities. You just have to take the time to memorize them.
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    I’m sure we have some future Einsteins here, but reading all this makes me want to cry. Either Finland is nuts for making you take trig/calc in 8th grade or you’re insanely smart. I’m hoping for the latter.
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    Just study and study. You'll see some positive results. I'd definitely recommend using SOHCAHTOA for trigonomentry like someone previously stated. It'd also be helpful if you elaborated more in what your struggling with or what you think you need help with. Also try using your resources like Youtube, we're at an advantage these days for having them!
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    Master Sorcerer LilDreamers's Avatar
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    Quote Originally Posted by YumYumCookie View Post
    I’m sure we have some future Einsteins here, but reading all this makes me want to cry. Either Finland is nuts for making you take trig/calc in 8th grade or you’re insanely smart. I’m hoping for the latter.
    We have trig in 9th grade and calc in 1st grade of Finnish high school (age 16-17)

    I am 14, not really smart but I have skipped a grade. And yes I knew the SOH CAH TOA thing already, I watched trig videos on Khan Academy. I just have passion for math haha.

    School starts at age 7 and ends the year people turn 16 (expect for people that have been held back/skipped grade/s)

    So it is kind of 9th grade in US, idk really




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    Quote Originally Posted by LilDreamers View Post
    I am studying both of them, help me please -A 8th grader from Finland
    I don’t encounter any difficulties on trigonometry and it is really important because it affects other topics like logarithms, differentiation, integration, graphs and more...


    For calculus, idk anything...
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    Quote Originally Posted by Farmers2168 View Post
    I don’t encounter any difficulties on trigonometry and it is really important because it affects other topics like logarithms, differentiation, integration, graphs and more...


    For calculus, idk anything...
    differentiation and integration is calculus thanks anyway
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    Attached here is a 292-page PDF about Basic Calculus, I used it when I was Grade 10-12 and it worked pretty well for me. Easily understandable and makes your life easier.

    http://www.math.nagoya-u.ac.jp/~rich...icCalculus.pdf

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    Master Sorcerer LilDreamers's Avatar
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    Quote Originally Posted by Maroczy View Post
    Attached here is a 292-page PDF about Basic Calculus, I used it when I was Grade 10-12 and it worked pretty well for me. Easily understandable and makes your life easier.

    http://www.math.nagoya-u.ac.jp/~rich...icCalculus.pdf
    thanks! I already got a calculus textbook but its pretty big so its this one
    Last edited by LilDreamers; 04-02-2019 at 01:52 PM.
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    Some people have curly brown hair through proper brushing.

    Some people have

    Sin=perp/hup

    Curly brown hair
    Cos=Base /gyp

    Tan=perp/Base
    Through proper brushing
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    sin2x + cos2x = 1

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    Calculus is pretty once you understand the concepts, all I can say is just keep practicing easy questions until you understand what the question is asking and how fast you can complete them

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    Very important to know and UNDERSTAND the definition of a derivative:

    f'(x) = d/dx (f(x))

    = lim dx-> 0 ((f(x + dx) - f(x))/dx)

    Mess around with it, try to find some derivatives of some functions (for beginners, try x^2 and x^3). Once you play with it, it'll become really fun and you'll start to find some clever way to mess with limits. If you think you're good enough, try deriving the exponent rule (d/dx (x^n) = n.x^(n-1)

    For starters, I thoroughly recommend you to watch 3Blue1Brown's video series on YouTube called 'Essence of Calculus'.

    Leave integral for now, understanding derivatives and playing with limits are what's important for now.
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    Master Sorcerer MadameZ's Avatar
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    Trigonometry:
    So basically, when you have a circle centered at the origin with a radius of one, you have a unit circle. A unit circle is useful for defining your trig stuff.

    To start, I'll just define radians for you:
    Radians are the angle at which the arclength of a sector is equal to a radius. In a complete circle, there are 2pi radians.

    So, when you have an angle along a circle, you'll have a point on the circle.
    Basically, the y value of this circle over the radius (or just the y value in the case of a unit circle) is called sine. x value is cosine. y / x is tangent. Just divide them from one (as in 1/y, 1/x) for cosecant, secant, and cotangent. This is triggering basics, and I don't feel like writing up a ton of identities for you. You're better off getting a basic overview on the concepts instead of getting listed specifics like sin^2x + cos^2x =1 or other silly things like sohcahtoa (which is also very googlable fyi).

    Calculus:
    Calculus is kinda based on the concept of limits, and how as you infinitely approach something, it may approach, but never equal to, a value. For example, on rational functions, horizontal asymptotes generally have a limit of the asymptote, as the function infinitely approaches that asymptote, never equalling it, but getting so close that it may as well be that value. This concept is used to define derivatives and integrals.
    Derivatives are the instantaneous rate of change of a function at a certain point. This means that you're finding the line tangent to a curve.
    So, how does this have to do with limits?
    You know the slope formula, right? (i hope you do). Y2-Y1/X2-X1. Now say that the difference in x is zero. You'll have y2-y1/h (h being the change in x). Congrats, now take the limit as h infinitely approaches 0 of that formula and you have the instantaneous rate of change, or the rate of change when the difference of x is zero, and also called the tangent line.
    There are a million different easier ways of finding a derivative of a function at an x value, but who cares? I'm just giving you the basics, as that's gonna do you better than simply being bombarded with googled facts.
    I guess it won't hurt to tell you what integrals are.
    Say that you have a function. You want to find the area under the function (or in general, funky areas).
    Well, draw rectangles that level off at the x axis under it and reach the y value at that x value.
    Good, following along?
    Now, imagine that there are an infinite amount of those rectangles, each with a width approaching 0.
    Now that's called an integral. I won't tell you much, just trying to show you the thinking that defines it.

    I hope I helped you with the basics, but it's really important to look at what you're working on now rather than looking for future content. It'll really do you good. You need to master any content before prior to moving on, as math is like building a building. You can't make a building without its foundations. Math is the same. You can't learn derivatives without limits, nor can you learn integrals without derivatives.
    Just my two cents. I just wrote all this on the top of my head lol.
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    Master Sorcerer Maroczy's Avatar
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    Quote Originally Posted by MadameZ View Post
    Trigonometry:
    So basically, when you have a circle centered at the origin with a radius of one, you have a unit circle. A unit circle is useful for defining your trig stuff.

    To start, I'll just define radians for you:
    Radians are the angle at which the arclength of a sector is equal to a radius. In a complete circle, there are 2pi radians.

    So, when you have an angle along a circle, you'll have a point on the circle.
    Basically, the y value of this circle over the radius (or just the y value in the case of a unit circle) is called sine. x value is cosine. y / x is tangent. Just divide them from one (as in 1/y, 1/x) for cosecant, secant, and cotangent. This is triggering basics, and I don't feel like writing up a ton of identities for you. You're better off getting a basic overview on the concepts instead of getting listed specifics like sin^2x + cos^2x =1 or other silly things like sohcahtoa (which is also very googlable fyi).

    Calculus:
    Calculus is kinda based on the concept of limits, and how as you infinitely approach something, it may approach, but never equal to, a value. For example, on rational functions, horizontal asymptotes generally have a limit of the asymptote, as the function infinitely approaches that asymptote, never equalling it, but getting so close that it may as well be that value. This concept is used to define derivatives and integrals.
    Derivatives are the instantaneous rate of change of a function at a certain point. This means that you're finding the line tangent to a curve.
    So, how does this have to do with limits?
    You know the slope formula, right? (i hope you do). Y2-Y1/X2-X1. Now say that the difference in x is zero. You'll have y2-y1/h (h being the change in x). Congrats, now take the limit as h infinitely approaches 0 of that formula and you have the instantaneous rate of change, or the rate of change when the difference of x is zero, and also called the tangent line.
    There are a million different easier ways of finding a derivative of a function at an x value, but who cares? I'm just giving you the basics, as that's gonna do you better than simply being bombarded with googled facts.
    I guess it won't hurt to tell you what integrals are.
    Say that you have a function. You want to find the area under the function (or in general, funky areas).
    Well, draw rectangles that level off at the x axis under it and reach the y value at that x value.
    Good, following along?
    Now, imagine that there are an infinite amount of those rectangles, each with a width approaching 0.
    Now that's called an integral. I won't tell you much, just trying to show you the thinking that defines it.

    I hope I helped you with the basics, but it's really important to look at what you're working on now rather than looking for future content. It'll really do you good. You need to master any content before prior to moving on, as math is like building a building. You can't make a building without its foundations. Math is the same. You can't learn derivatives without limits, nor can you learn integrals without derivatives.
    Just my two cents. I just wrote all this on the top of my head lol.
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