Trig+Identities

= Unit 6: Trigonometric Identities =
 * [[image:http://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/720px-Unit_circle_angles_color.svg.png width="384" height="384" align="center"]]

// **prerequisite skills and notes (Valerie) :** // __ concept review __
 * SO CAH TOA
 * RECIPROCAL TRIG RATIOS

Notice how a "co-(something)" trig ratio is always the reciprocal of some "non-co" ratio. You can use this fact to help you keep straight that cosecant goes with sine and secant goes with cosine. //sin//2(//t//) + //cos//2(//t//) = 1 //tan//2(//t//) + 1 = //sec//2(//t//) 1 + //cot//2(//t//) = //csc//2(//t//) The above, because they involve squaring and the number 1, are the "Pythagorean" identities. You can see this clearly if you consider the unit circle, where //sin//(//t//) = //y//, //cos//(//t//) = //x// , and the hypotenuse is 1. //sin//(–//t//) = –//sin//(//t//) //cos//(–//t//) = //cos//(//t//) //tan//(–//t//) = –//tan//(//t//)

**// Angle-Sum //** **//and -Difference Identities//** //sin//(α + β) = //sin//(α)//cos//(β) + //cos//(α)//sin//(β) //sin//(α – β) = //sin//(α)//cos//(β) – //cos//(α)//sin//(β) //cos//(α + β) = //cos//(α)//cos//(β) – //sin//(α)//sin//(β) //cos//(α – β) = //cos//(α)//cos//(β) + //sin//(α)//sin//(β)



__Videos and Summaries (Jonathan)__ [] Its a good video to help remember and derive the trigonometric identities. It helps with remembering the trig functions and their reciprocal functions as well. [] A really informative video that helps with verifying trigonometric identities and verifying trig equations using trig identities. [] A great video that helps with verifying equations by simplifying both sides of the equation using trig indentities. [] This video is great help if you dont understand multiplying by conjugates. It explains and helps you understand why and when you should use conjugates when verifying trig equations. =Review Problems (Drew)=

Beginner: Cosπ/6 Cosπ/3 + Sinπ/3 Sinπ/6 *use angle sum/difference identity
On The Way:Sin15°

Got It: Cos(13π/12)

Got It: Sin 75°

Rockstar: Sin 285°

Key

Beginner: √3/2

On The Way: (√6-√2)/4

Got it: (-√6-√2)/4

Got It: (√6+√2)/4

Rockstar: (-√6-√2)/4

(Madison Couch)

=**Barron's E-Z Math**=

Websites and Summaries ( Kahner ) [] - Great website showing multiple examples of adding, subtracting, multiplying and as well as verifying. Showing a step by step process to help get that confident feeling when solving any other problem. [] - A slideshow presentation giving all identities and shows step by step examples also fundamental notes that you might want to think abour writing down. [] - All Identities that are needed for solving all problems also helpful for memorizing the different formulas. [] - A website ranking what identities are important to know and others that are not as important as well as a description describing each identity and what it stands for.


 * Formulas & Theorems ( Tea' Denerson )**
 * @https://www.youtube.com/watch?v=425bdHkplJY**

A helpful link to my video on the formula and theorems of the Trig Identities Unit.

Careers and uses (Grant Goforth) __**Architecture**__: Trigonometric identities are found heavily in architecture. especially when developing large infrastructure. The six different identities are used to find either the length of one one or more sides of a shape, or the angle at which different materials should be placed at. It is common to find them when constructing blueprints for actual structures. __**Engineering**__: The six trigonometric identities are very prominent in several different types of engineering. Some of the more popular types of engineering where trigonometric identities are used are civil, electrical, and mechanical engineering. They are used when analyzing alternating and direct currents. The shape of the curves that are alternating and direct curves form correspond to that of the trigonometric identity curves.