Download 1.3 right triangle trigonometry

Right Triangle
Trigonometry
Unit Circle Definitions of the
6 Trig. Functions…
sin = y
cos = x
y
tan =
x
1
csc =
y
1
sec =
x
x
cot =
y
Non-Unit Circle Definitions of the
6 Trig. Functions…
y
sin =
r
x
cos =
r
y
tan =
x
r
csc =
y
r
sec =
x
x
cot =
y
y
sin =
r
x
cos =
r
These
definitions are
closely related
to the unit
circle
definition. In
the unit circle,
the radius is =
to 1, thereby
eliminating the
denominator.
(0,1)

(-1,0)

(2, 2)
(2/2, 2/2)
45

(0,-1)
(1,0) 
Since this
is a unit
circle
(radius of
one),
sin 45 = 2/2
Now, on
(2,0) this second
circle, the
radius is no
longer 1
unit (it’s 2).
Therefore,
sin 45 = y/r
or
sin 45 = 2/2
Let’s practice these definitions.
Find exact values of the six trig.
functions of the angle  shown in the
figure.
y
5
If
this
triangle
was
sin  =
=
r center
13
placed at the
(12,5) of a circle,
x
12

cos  = what
=
would the r
radius
of
13
13
y be?5
that circle
5
tan  =
=
2 = c2 12

a2 +bx
r 2 13
12
2
2
12 =
+5 = =
c
csc
169 =yc2 5
rc 13
13
=
cos  =
=
x
12
12
x
=
cot  =
5
y
Your Turn #1: Place your work in
your notebook.
Find exact values of the six trig.
functions of the angle  shown in the
figure.
5

5
Look back at the previous slide if you
need assistance.
Your Turn #2: Place your work in
your notebook.
Find exact values of the six trig.
functions of the angle  shown in the
figure.
4

8
Hint: Be sure to reduce radicals.
Let’s practice some more…
Sketch a right triangle corresponding
to the trig. function of the acute angle
. Then determine the other five trig.
functions of .
(5,2)

2
y
3
sin  =
=
2
3
r

x
5
5
2
2
2
=
cos

=
a + br = c
3
2
2
2
a +2 =3
y
25
2
a
+
4
=
9
=
tan  =
35
r
x
5
=
sec  =
a2 = 5
5
x
ra = 53
x
5
=
csc  =
cot  =
=
y
2
y
2
Your Turn #3: Place your work in
your notebook.
Sketch a right triangle corresponding
to the trig. function of the acute angle
. Then determine the other five trig.
functions of .
Think
sec  = 4
sec  = 4/1
Look back at the previous slide if you
need assistance.
Your Turn #4: Place your work in
your notebook.
Sketch a right triangle corresponding
to the trig. function of the acute angle
. Then determine the other five trig.
functions of .
9
csc  =
5
Look back if you need assistance.
What is SOH CAH TOA?
This is another way of
remembering the definitions of
the trigonometric functions.
SOH opposite
sin  =
hypotenuse
Hyp.

Opp.
What is SOH CAH TOA?
CAH
adjacent
cos  =
hypotenuse
Hyp.

Adj.
What is SOH CAH TOA?
TOA
opposite
tan  =
adjacent
Opp.

Adj.
Assignment:
pg. 156: 1-26