The Sharkasm Empire

Would you like to react to this message? Create an account in a few clicks or log in to continue.
The Sharkasm Empire

The Sharkasm Empire is a wonderful community brought to you by the Sharks of Sharkasm

Top posting users this month

No user

Latest topics

» Food Food Food
Chemical Engineering. - Page 2 EmptyWed 10 Jan 2024, 3:34 pm by TheCryptKeeper

» "It's the door..... To the light" - The Social Thread v 2.0
Chemical Engineering. - Page 2 EmptyWed 10 Jan 2024, 3:29 pm by TheCryptKeeper

» Diary of a Mac Student
Chemical Engineering. - Page 2 EmptyTue 25 Apr 2023, 2:41 pm by TheCryptKeeper

» Arcasia: Legend of the Wolfram Emerald
Chemical Engineering. - Page 2 EmptyTue 25 Apr 2023, 11:56 am by lil' poopie boy

» Le Cinéma
Chemical Engineering. - Page 2 EmptyThu 20 Apr 2023, 11:08 am by TheCryptKeeper

» Ideas
Chemical Engineering. - Page 2 EmptySat 15 Apr 2023, 8:49 am by lil' poopie boy

» Musique Lystoux
Chemical Engineering. - Page 2 EmptyFri 14 Apr 2023, 8:59 am by TheCryptKeeper

» Through Shady Lanes
Chemical Engineering. - Page 2 EmptyThu 13 Apr 2023, 8:26 pm by lil' poopie boy

» King of All Ratings Thread
Chemical Engineering. - Page 2 EmptyThu 13 Apr 2023, 5:36 pm by TheCryptKeeper

» Where's The Beats!?
Chemical Engineering. - Page 2 EmptyMon 21 Aug 2017, 7:42 pm by Italyins


4 posters

    Chemical Engineering.

    Cephalo the Pod
    Cephalo the Pod
    Charles Babbage


    Posts : 1796
    Reputation : 8
    Join date : 2012-08-22
    Age : 29
    Location : Somewhere in London, jogging.

    Chemical Engineering. - Page 2 Empty Aw, geez, math on a keyboard.

    Post by Cephalo the Pod Mon 22 Aug 2016, 12:55 am

    Lesson 0 - High School Stuff (Part 7: Trigonometric Identities)
    A trigonometric identity is a relation betweem two different mathematical functions that involve trigonometric functions such as sin(x). They come in handy when simplifying mathematical expressions.

    So you know how sin(x)=opposite/hypotenuse of an angle on a right-angle triangle, right? And cos(x)=adjacent/hypotenuse, and tan(x)=opposite/adjacent?
    Chemical Engineering. - Page 2 Adjacent-opposite-hypotenuse

    Well there's three others:

    • csc(x)=H/O=1/sin(x). This is the cosecant.
    • sec(x)=H/A=1/cos(x). This is the secant.
    • cot(x)=A/O. This is the cotangent.


    Hey, let's look back to Pythagorus's Theorem. O^2+A^2=H^2. We can get three trigonometric identities from this:

    • Divide by H^2 on both sides. That gets you [sin(x)]^2+
      [cos(x)]^2=1.
    • Divide by A^2 on both sides. That gets you [tan(x)]^2+1=[sec(x)]^2.
    • Divide by O^2 on both sides. That gets you 1+[cot(x)]^2=[csc(x)]^2.

    Honestly, only the first of those really gets used.

    Another useful set of identities is the dual-angle identities. When you have a trigonometric function where the input involves two angles, you can convert it into a different expression, and vice versa.
    Chemical Engineering. - Page 2 665px-AngleAdditionDiagramSine.svg
    Chemical Engineering. - Page 2 600b028031a41e3d9e37fcd38c2af048374d496d
    Chemical Engineering. - Page 2 Bc293268efaf69be2b7e0c4173c39d86f4945373
    These identities are helpful when, for example, you know the value of one angle but not the other.


    Last edited by Cephalo the Pod on Mon 22 Aug 2016, 2:44 pm; edited 5 times in total
    Cephalo the Pod
    Cephalo the Pod
    Charles Babbage


    Posts : 1796
    Reputation : 8
    Join date : 2012-08-22
    Age : 29
    Location : Somewhere in London, jogging.

    Chemical Engineering. - Page 2 Empty Aw, geez, math on a keyboard.

    Post by Cephalo the Pod Mon 22 Aug 2016, 12:58 am

    And I THINK that covers just about all the high school stuff needed to understand Chem. Eng.

    I think I'll start with the university-level math next, and then some basic kinematics.


    Last edited by Cephalo the Pod on Mon 22 Aug 2016, 2:52 pm; edited 2 times in total
    TheCryptKeeper
    TheCryptKeeper
    Wolfram Knight


    Posts : 2004
    Reputation : 19
    Join date : 2012-08-21
    Age : 29
    Location : 4 levels up and 1 room to the left

    Chemical Engineering. - Page 2 Empty Re: Chemical Engineering.

    Post by TheCryptKeeper Mon 22 Aug 2016, 12:02 pm

    why not just edit the other post?
    Cephalo the Pod
    Cephalo the Pod
    Charles Babbage


    Posts : 1796
    Reputation : 8
    Join date : 2012-08-22
    Age : 29
    Location : Somewhere in London, jogging.

    Chemical Engineering. - Page 2 Empty Aw geez, I hope that made sense.

    Post by Cephalo the Pod Sat 27 Aug 2016, 12:01 am

    Here we go

    Applied Mathematics - Integration
    So sometimes you wanna calculate the area under the curve. Specifically, a certain portion of the area under a curve, stretching from one x-value to another. An integral. This can be reinterpreted as calculating the area of an infinite number of infinitely thin rectangles that each extend to the curve.

    With each rectangle, you're multiplying a y-value by an infinitely small difference in two x-values. Sound familar? It's essentially the opposite of a derivative, where you're dividing by a small difference in x-values. This is why calculating an integral means finding the antiderivative of the equation you're given.

    Example: x^n, where n is a constant that isn't -1. The derivative would be n*x^(n-1). So the antiderivative would be [x/(n+1)]*x^(n+1).
    • If the integral you're calculating has two specific end points, you calculate the value ls of the integral equation at both end points, and then you subtract the value at the first end point from the value at the second end point.
    • If you have no specific end points, you need to add a nondescript constant to the integral equation, because something like that won't affect the original derivative.
    TheCryptKeeper
    TheCryptKeeper
    Wolfram Knight


    Posts : 2004
    Reputation : 19
    Join date : 2012-08-21
    Age : 29
    Location : 4 levels up and 1 room to the left

    Chemical Engineering. - Page 2 Empty Re: Chemical Engineering.

    Post by TheCryptKeeper Thu 01 Sep 2016, 4:39 pm

    calculus is so sick. math is just a beaut dude.

    Sponsored content


    Chemical Engineering. - Page 2 Empty Re: Chemical Engineering.

    Post by Sponsored content


      Current date/time is Thu 28 Mar 2024, 8:36 pm