Talk:2070: Trig Identities

I am confused by the insect line. This seems to be true only if s=t. 141.101.96.209 19:03, 9 November 2018 (UTC)

I added a note regarding how similar it sounds to 'sinsec'. 172.68.51.154 01:47, 10 November 2018 (UTC)

That one and the `cas` aren't making any sense to me. GreatBigDot (talk) 20:02, 9 November 2018 (UTC)

Oh, the casinus is much important to... What was it? --Dgbrt (talk) 20:15, 9 November 2018 (UTC)

cas is realtively easy... it is cos(theta)=a/c -> cs(theta)=ao/c -> cas(theta)=o/c; when you realise that the top one isn't zero but o it clicks 141.101.96.209 23:35, 9 November 2018 (UTC)

You made the same error Randall did: you divided by 'o' on the left and multiplied on the right. I think the theme of the page is expanding significantly upon common math errors that were already humorous, like the common proof of 5=3 by dividing and multiplying by zero. The error here is in line with the theme of casual beginner errors. 172.68.51.154

You can see cin is derived from sin by swapping the positions of c and s. Likewise, Switching the a and o in cos(theta) = a/c gives cas(theta) = o/c i.e. no need for multiplicative consistency. The rule of treating things as a product of terms is implemented fully in the following lines. 162.158.91.83 11:23, 12 November 2018 (UTC)

$sin \theta = b/c$ leading to $cin \theta = b/s$ is algebraically valid if you interpret sin as the product of s, i, n by multiplying both sides by c/s. It is not valid to just "swap" two letters in one equation that is part of a system of equations. You could do the same trick and get $cas \theta = a^2/oc$ from $cos \theta = a/c$ or start with $sec \theta = c/a$ and get $cas \theta = c/e$. Note for all equations except $cas \theta = o/c$ and switching an $s$ to a $t$ to find $tan \theta = insect \theta^2$, the equations can be correctly derived by treating trig functions as product of single letter variables and algebraically manipulating them. Jimbob (talk) 16:59, 12 November 2018 (UTC)

I think insect is.. a bug.. ;) Smerriman (talk) 20:18, 9 November 2018 (UTC)

Is Enchant at target a magic:the gathering reference? AncientSwordRage (talk) 20:55, 9 November 2018 (UTC)

I think it is a Magic: The Gathering reference. Although it is phrased oddly. You'd think it would be "at target enchantment", rather than "target at enchantment". --Dryhamm (talk) 21:04, 9 November 2018 (UTC)

Likely, it refers to the bigbox retailer, Target. 172.68.58.233 (talk) (please sign your comments with ~~~~)

To me it sounds more like a reference to a nerdy video game, where a certain object worked like this, turning e.g. BEAM OF DARK ENERGY into a BAKED FERRY GNOME 108.162.246.11 21:53, 12 November 2018 (UTC)

Voila - s=t. -- Elliott (talk) (please sign your comments with ~~~~)

That was incredible! (assuming previous poster discovered the extrapolated proof in the description) 172.68.51.154 01:47, 10 November 2018 (UTC)

Combining $\cos\theta=\frac{a}{c}$ and $\mathrm{cas}\ \theta=\frac{o}{c}$ allows you to conclude $a^2 = o^2$, not $a=o$. 162.158.146.10 (talk) (please sign your comments with ~~~~)

Somebody added a comment on puns, e.g. that "cin sucks". More explanation is needed. It looks like some kind of a meta-joke. If you ask why, and start interpreting, you see that "b/c" == "because". It might be the answer to why the puns line should be removed, though. 172.68.51.154

For the Bot->Boat->Stoat line, this comes from the word game where you add/change letters to make a new word. Start with bot=a/c, multiply by a on both sides gets boat=a^2/c. Multiply by st on both sides and divide b on both sides gets Stoat=a^2/c*St/b. 162.158.78.166 (talk) (please sign your comments with ~~~~)

Uh... people... THE NAME GAME? Hello? https://en.wikipedia.org/wiki/The_Name_Game 162.158.79.107 (talk) (please sign your comments with ~~~~)

Checking through the math, just working from the real trig identities, without considering Randall's at-first-glance questionable identities like cas theta = o/c, basically everything that does not have a factor of d or 2 in it is equal to 1, and d is equal to 1/2, which then establishes the more questionable identities as tautological, 1=1. 162.158.142.100 04:09, 10 November 2018 (UTC)

$\sec\theta = sect \eta$ 141.101.104.71 13:36, 10 November 2018 (UTC) AndreasH

Am I the only one who saw t²n²a⁴ as "tuna"? 172.68.58.233 14:17, 10 November 2018 (UTC)

Yes. 162.158.75.190 (talk) (please sign your comments with ~~~~)

$\frac{d}{dx}\sec x=\sec x\tan x=$ sex tanks. Probably not Douglas Hofstadter (talk) 21:36, 11 November 2018 (UTC)

I thought "distance 2 banana" had to be a reference to QBasic's Gorillas game. "Enchant at target" could refer to the banana exploding when it hits something. mrpsbrk 162.158.123.91 (talk) (please sign your comments with ~~~~)

From when I saw $cin\theta$ I knew the rest of the comic would be $\frac{b}{s}$. Observer of the Absurd (talk) 13:28, 15 May 2019 (UTC)

List of Essential Trigonometry formulas for Class 10, 11, and 12

Trigonometry formulas (source:https://inspiria.edu.in/trigonometry-formulas-for-class-12/) If you are looking for the complete list of all trigonometry formulas for classes 10, 11, and 12, we have made it completely easy for you to understand and learn all trigonometry formulas and ratios to a single page. Memorizing these trigonometric formulas help students to solve trigonometry problems easily, which further leads to a good score in Mathematics. For easy understanding and access, we have provided the trigonometry table and inverse trigonometry formulas. Trigonometry, a word derived from the Greek words ‘Trigon’ and ‘Metron’ refers to ‘measuring the sides of a triangle. This branch of mathematics studies the relation between angles and sides of triangles. Trigonometry formulas are used widely in various fields and have been in use since the 3rd Century BC. From Navigation to Celestial Mechanics to Engineering, Architecture and other various fields trigonometry play a vital role. Various geometrical problems are solved using the trigonometry ratios Sine (Sin), Cosine (Cos), Tangent (Tan), Cotangent (cot), Secant (sec), and Cosecant (Csc), product identities, Pythagorean Identities, etc. There are several Trigonometric functions, formulas, and ratios like the sign of ratios in different quadrants, sum identities, difference identities, cofunction identities, double angle identities, half-angle identities, etc. These are introduced from Class 10th and the concept is further explained in classes 11th & 12th. Trigonometry Formulas for Class 10, 11, and 12: As trigonometry is the study of relationships between angles and sides of the triangles. The primary triangle studied is the right triangle. In a right-angled triangle, the three sides are named Hypotenuse, Opposite, and Adjacent. The longest side is called the Hypotenuse, the opposite side to the angle is called the Perpendicular (Opposite), and the side where both hypotenuse and opposite sits is the adjacent side. Basic Formulas Reciprocal Identities Trigonometry Table Periodic Identities Co-function Identities Sum and Difference Identities Double Angle Identities Triple Angle Identities Half Angle Identities Product Identities Sum to Product Identities Inverse Trigonometry Formulas

Basic Formulae The basic Trigonometry formulas for class 10 are six basic ratios which are used for finding the elements in trigonometry which are called trigonometric functions. These are Sine (Sin), Cosine (Cos), Tangent (Tan), Cotangent (Cot), Secant (Sec), and Cosecant (Csc). By taking right triangle as a reference, these Trigonometry functions are derived as following: sin θ = Opposite Side/Hypotenuse cos θ = Adjacent Side/Hypotenuse tan θ = Opposite Side/Adjacent Side sec θ = Hypotenuse/Adjacent Side cosec θ = Hypotenuse/Opposite Side cot θ = Adjacent Side/Opposite Side Reciprocal Identities Reciprocal identities are given as following: cosec θ = 1/sin θ sec θ = 1/cos θ cot θ = 1/tan θ sin θ = 1/cosec θ cos θ = 1/sec θ tan θ = 1/cot θ These are taken from a right-angled triangle. As the height and base of the right triangle are given, we can find out the Sine (sin), Cosine (cos), Tangent (tan), Cotangent (cot), Secant (sec), and Cosecant (CSC) values using trigonometric formulas. These reciprocal trigonometric identities can also be derived by using the trigonometric functions. Trigonometry Table Below is the table for trigonometry formulas for angles that are commonly used for solving problems. Angles (In Degrees) 0° 30° 45° 60° 90° 180° 270° 360° Angles (In Radians) 0° π/6 π/4 π/3 π/2 π 3π/2 2π sin 0 1/2 1/√2 √3/2 1 0 -1 0 cos 1 √3/2 1/√2 1/2 0 -1 0 1 tan 0 1/√3 1 √3 ∞ 0 ∞ 0 cot ∞ √3 1 1/√3 0 ∞ 0 ∞ csc ∞ 2 √2 2/√3 1 ∞ -1 ∞ sec 1 2/√3 √2 2 ∞ -1 ∞ 1

Periodicity Identities in Radian After the basic formulas Trigonometry formula for Class 11 introduces periodicity Identities used in shifting the trigonometric functions by one period to the left or right. These are called co-function identities. sin (π/2 – A) = cos A & cos (π/2 – A) = sin A sin (π/2 + A) = cos A & cos (π/2 + A) = – sin A sin (3π/2 – A) = – cos A & cos (3π/2 – A) = – sin A sin (3π/2 + A) = – cos A & cos (3π/2 + A) = sin A sin (π – A) = sin A & cos (π – A) = – cos A sin (π + A) = – sin A & cos (π + A) = – cos A sin (2π – A) = – sin A & cos (2π – A) = cos A sin (2π + A) = sin A & cos (2π + A) = cos A We know tall trigonometry functions in Class 11 are repetitive in nature, repeating themselves after this periodicity constant. This periodicity constant is different for different trigonometric identities. tan 45° = tan 225° but this is also true for cos 45° and cos 225°. Co-function Identities (in Degrees The co-function or periodic identities can also be represented in degrees as: sin(90°−x) = cos x cos(90°−x) = sin x tan(90°−x) = cot x cot(90°−x) = tan x sec(90°−x) = csc x csc(90°−x) = sec x Sum & Difference Identities sin(x+y) = sin(x)cos(y)+cos(x)sin(y) cos(x+y) = cos(x)cos(y)–sin(x)sin(y) tan(x+y) = (tan x + tan y)/ (1−tan x •tan y) sin(x–y) = sin(x)cos(y)–cos(x)sin(y) cos(x–y) = cos(x)cos(y) + sin(x)sin(y) tan(x−y) = (tan x–tan y)/ (1+tan x • tan y) Double Angle Identities sin(2x) = 2sin(x) • cos(x) = [2tan x/(1+tan2 x)] cos(2x) = cos2(x)–sin2(x) = [(1-tan2 x)/(1+tan2 x)] cos(2x) = 2cos2(x)−1 = 1–2sin2(x) tan(2x) = [2tan(x)]/ [1−tan2(x)] sec (2x) = sec2 x/(2-sec2 x) csc (2x) = (sec x. csc x)/2 Triple Angle Identities Sin 3x = 3sin x – 4sin3x Cos 3x = 4cos3x-3cos x Tan 3x = [3tanx-tan3x]/[1-3tan2x]