Download Title: May 59:36 AM (1 of 6)

That um triangle um
always knows the um
correct um answer. um
I'm the RIGHT
triangle
Mathematicians often use greek letters when working with trigonometry
­ this is the Greek letter 'theta' Trigonometry ­ From the Greek trigonon = three angles and
metro = measure.Trigonometry is a part of elementary mathematics dealing with
angles, triangles, and trigonometric functions
Ratios of a right triangle's three sides are
used to define the six trigonometric
functions: Sine, cosine, tangent, cosecant,
secant, and cotangent. These six functions
are abbreviated sin, cos, tan, csc, sec, cot, respectively.
se
nu
ote
p
hy
adjacent side
Right Triangle definitions of trigonometric functions
Let be an acute angle of a right triangle. The six trigonometric
functions of are defined as follows.
The abbreviations, opp, adj, and hyp represent the lengths
of the three sides of the right triangle. Note that the ratios in the second row are the reciprocals of the ratios in the first row.
Example 1. Evaluate the six trigonometric functions of the angle shown in the right triangle.
hypontenuse
3
4
Title: May 5­9:36 AM (1 of 6)
Opposite
side
You know Chief... Geronomo, Tecumseh,
crazy horse and Chief Wahoo.
Rudolph the red nose
reindeer music
Geronomo
Tecumseh
Chief Wahoo
Crazy Horse
But do you recall... The most famous indian chief of all?!?
Title: May 6­9:46 AM (2 of 6)
Sine of hatchet
= opposite over
hypotenuse
um
Chief SohCahToa
The trigonometric Indian chief
had a very shiny hatchet.
and when he threw it using properties of trigonometry
he always hit his target.
Title: May 6­9:50 AM (3 of 6)
The angles, 30, 45, 60, occur frequently in trigonometry.
The table below gives the values of the six trigonometric functions for these angles. To remember these values, you may find it
easier to draw the triangles shown, rather than memorize the table.
sin
cos
Title: May 5­10:08 AM (4 of 6)
Gee I'
m
m
Fro
a Tree
You saw special right triangles
1) 45o ,45o, 90o
and
}
2) 30o, 60o, 90o
The ratios of
their sides
Where do these go?
2)
1)
30o
2
2
3
1
45o
1
1
60o
45o
Example 2 Find the value of x
10
60
x
Find Example 3
3
Assignment Page 772, 1, 4 - 24 even and 25 - 32
6
Title: Apr 29­7:39 AM (5 of 6)
Trig functions can be used to find a missing side length or
angle measure of a right triangle. Finding ALL missing side
lengths and angle measures is called SOLVING A RIGHT
TRIANGLE
Ex 4)Using a calculator to Solve a Right Triangle.
B
c
a
19o
A
C
b = 13
Note: Upper case VS lower case letters and relationship of sides to angles
C
B
A
9) page 772
#5) page 772
A = 75o c = 20
c
6
Ѳ
b
8
Find missing side lengths in simplest radical form
x
23) page 773
Normal ratio 1, 1, 2
45o
y
11
Title: Apr 29­7:57 AM (6 of 6)
a
Attachments
Christmas_Carols_­_Rudolph_The_Red_Nosed_Reindeer.mid