Transcript document

Warmup: What is wrong
with this?
30⁰
8.3 and 8.4
Trigonometric
Ratios
Finding Trig Ratios
• A trig ratio is a ratio of the lengths of
two sides of a right triangle.
• The word trigonometry is derived from
the ancient Greek language and means
measurement of triangles.
• The three basic trig ratios are sine,
cosine, and tangent.
• Abbreviated as sin, cos, and tan
respectively
Trigonometric Ratios
• Let ∆ABC be a right
triangle. If you are
standing from angle
A, the following sides
are labeled:
opposite, adjacent
and hypotenuse
B
hypotenusec
A
b
side adjacent to angle A
cos A =
adjacent
Side
a opposite
angle A
C
=
hypotenuse
sin A =
opposite
hypotenuse
=
b
c
a
c
tan A =
opposite
adjacent
=
a
b
Trigonometric Ratios
• If you were standing
at angle B, you
would have to relabel the sides of
opposite, adjacent
and hypotenuse
B
hypotenusec
A
b
side opposite to angle B
cos B =
adjacent
Side
a adjacent
angle B
C
=
hypotenuse
sin B =
opposite
hypotenuse
=
a
c
b
c
Tan B =
opposite
adjacent
=
b
a
The famous Indian…
SOHCAHTOA
Ex. 1: Find sin, cos and tan of angle S
Ratio
sin S =
cosS =
tanS =
opposite
S
R
hypotenuse
adjacent
13
5
hypotenuse
opposite
adjacent
T
12
S
Ex.2: Find the sin, cos and tan of angle R
Ratio
sin R =
cosR=
tanR =
R
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
R
13
5
T
12
S
Using the Inverse
• You can use the sin, cos and tan ratio and
calculate it’s inverse, sin-1, cos-1, tan-1 to find
the measure of the angle.
• Make sure your calculator is in degree mode!!!
*make note: sin, cos, and tan are ratios.
Inverses find angles!!!
Let’s find angle S.
Ratio
sin S =
cosS =
tanS =
opposite
S
R
hypotenuse
adjacent
13
5
hypotenuse
opposite
adjacent
T
12
S
Now let’s find the angle measure from a
previous example
Ratio
sin R =
cosR=
tanR =
R
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
R
13
5
T
12
S
Examples: Given the triangles below,
find the missing angle measure to the
nearest degree
6
2
6
8
?
10
?
Practice: Solve for the
missing variables
1.)
2.)
7
12
x⁰
26⁰
m
16
9
3.)
30
4.)
y
z
p
15
40⁰
(No decimal answers in 4)