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.