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Trigonometry

- Introduction

Instant Trig

- Trigonometry is math, so many people find it

scary - Its usually taught in a one-semester high-school

course - However, 95 of all the trig youll ever need

to know can be covered in 15 minutes - And thats what were going to do now

Angles add to 180

- The angles of a triangle always add up to 180

Right triangles

- We only care about right triangles
- A right triangle is one in which one of the

angles is 90 - Heres a right triangle

Heres the right angle

hypotenuse

opposite

adjacent

- We call the longest side the hypotenuse
- We pick one of the other angles--not the right

angle - We name the other two sides relative to that angle

The Pythagorean Theorem

- If you square the length of the two shorter sides

and add them, you get the square of the length of

the hypotenuse - adj2 opp2 hyp2

- 32 42 52, or 9 16 25
- hyp sqrt(adj2 opp2)
- 5 sqrt(9 16)

5-12-13

- There are few triangles with integer sides that

satisfy the Pythagorean formula - 3-4-5 and itsmultiples (6-8-10, etc.)are the

best known - 5-12-13 and its multiples form another set

- 25 144 169

Ratios

- Since a triangle has three sides, there are six

ways to divide the lengths of the sides - Each of these six ratios has a name (and an

abbreviation) - Three ratios are most used
- sine sin opp / hyp
- cosine cos adj / hyp
- tangent tan opp / adj
- The other three ratios are redundant with these

and can be ignored

- The ratios depend on the shape of the triangle

(the angles) but not on the size

Using the ratios

- With these functions, if you know an angle (in

addition to the right angle) and the length of a

side, you can compute all other angles and

lengths of sides

- If you know the angle marked in red (call it A)

and you know the length of the adjacent side,

then - tan A opp / adj, so length of opposite side is

given by opp adj tan A - cos A adj / hyp, so length of hypotenuse is

given by hyp adj / cos A

The Hard Part

- If you understood this lecture, youre in great

shape for doing all kinds of things with basic

graphics - Heres the part Ive always found the hardest
- Memorizing the names of the ratios
- sin opp / hyp
- cos adj / hyp
- tan opp / adj

Mnemonics from wikiquote

- The formulas for right-triangle trigonometric

functions are - Sine Opposite / Hypotenuse
- Cosine Adjacent / Hypotenuse
- Tangent Opposite / Adjacent
- Mnemonics for those formulas are
- Some Old Horse Caught Another Horse Taking Oats

Away - Saints On High Can Always Have Tea Or Alcohol