Geometry 4/7/14 Obj: SWBAT use trig ratiosChapter 8 Take Home TestAgenda•Bell Ringer: Go over Quiz•pg 450 #4-8 •Homework Requests: pg 699 #1-4, pg 694 #1-14•Homework: •Chapter 8 Take Home Test; Due Thursday

Announcements:

Introduction to TrigonometryFinding sides from angles

Trigonometry is…• A branch of geometry used first by the

Egyptians and Babylonians (Iraq)

• Used extensively is astronomy and building

• Based on ratios between angles in RIGHT Triangles

The ratios have names and abbreviations…

Ratio Name

sine

cosine

tangent

cotangent

secant

cosecant

Abbreviation

sin

cos

tan

cot

sec

csc

The Trigonometric (trig) ratios: FUNCTION INVERSE FUNCTION

ac

bside adjacent to angle A

Sideoppositeangle A

hypotenuse

A

B

C

Also true are…

Here we name one angle Theta Is the Greek letter Theta

We could ask for the trig functions of the angle by using the definitions.

a

b

c

You MUST get them memorized. Here is a mnemonic to help you.

The sacred Jedi word:

SOHCAHTOA

c

b

hypotenuse

oppositesin

adjacentcos

hypotenuse

a

c opposite

tanadjacent

b

a

opposite

adjacent

SOHCAHTOA

If you know the sine, cosine, or tangent of an acute angle measure, you can use the inverse trigonometric functions to find the measure of the angle.

!IMPORTANT!

To solve trig functions in the calculator,

make sure to set your MODE to DEGREES

• Directions:

Press MODE, arrow down to Radian

Arrow over to Degrees

Press ENTER

Example: Find the missing side lengths.

You try:

• Find the hypotenuse length and the values of the 5 other trig functions for:

Hint: use a2 + b2 = c2 to find the hypotenuse!

Did you get…

Why is this useful?

• Imagine being an Ancient Egyptian. They had no calculators, no computers. They could use one angle and a pyramid’s side length to find the other side lengths.