__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?

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.

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

Thu 01 Mar 2018, 11:08 pm by Alpha Delfa

» Where's The Beats!?

Mon 21 Aug 2017, 7:42 pm by Italyins

» Musique Lystoux

Fri 11 Aug 2017, 3:16 pm by TheCryptKeeper

» Le Cinéma

Tue 25 Jul 2017, 12:26 am by Italyins

» The TSEmpire Book Club!

Mon 24 Jul 2017, 8:28 pm by TheCryptKeeper

» The Beautiful Young Pictures thread

Mon 24 Jul 2017, 8:25 pm by TheCryptKeeper

» The Anime Thread

Fri 21 Jul 2017, 3:02 pm by Italyins

» The Collective Dream Journal

Thu 20 Jul 2017, 8:26 pm by Vyzor

» The Internet Video Discussion Thread

Thu 20 Jul 2017, 7:52 pm by Vyzor

» The Official Summer Beats Thread!

Mon 17 Jul 2017, 5:17 pm by lil' poopie boy