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Geometry Lesson 9.5A
Trigonometric Ratios
Warm-Up: Ratios of Triangle Sides
NEED A VOLUNTEER!
 Calculate the ratios in the table below
 Are the triangles similar? Why?
 What is true of the ratios in the table?

Triangle
Big
Small
a
b
c
a
c
b
c
a
b
Trigonometric (“Trig”) Ratios
 Trig
ratio: The ratio of the lengths of
two sides of a right triangle
 There are three basic trig ratios: sine,
cosine, and tangent
 These are abbreviated:
 Sine  sin
 Cosine  cos
 Tangent  tan
Sine, Cosine, Tangent

The sine, cosine, and
tangent of angle A are:
A
cos A =
side adjacent A b

hypotenuse
c
tan A =
side opposite A a

side adjacent A b
c
opposite
sin A =
side opposite A a

hypotenuse
c
B
adjacent
b
Notice that sin,
cos, and tan
operate on
angles
a
C
SOH-CAH-TOA!
 SOH:
Sine is Opposite over
Hypotenuse
 CAH:
Cosine is Adjacent over
Hypotenuse
 TOA:
Tangent is Opposite over
Adjacent
Finding Trig Ratios
Use the right
triangles to find the
specified trig ratios
a
sin A =
c
b
b
tan B =
cos A =
a
c
a
sin J =
tan A =
b
k
b
cos J =
sin B = c
l
a
tan J =
cos B =
c

j
l
j
k
Finding Trig Ratios

Find the sine, cosine, and tangent for each
acute angle (round to 4 decimal places)
1.
2.
3.
•sin F = 3/5 = 0.6
•cos F = 4/5 = 0.8
•tan F = 3/4 = 0.75
•sin D = 4/5 = 0.8
•cos D = 3/5 = 0.6
•tan D = 4/3 = 1.3333
•sin D =
•cos D =
•tan D =
•sin F =
•cos F =
•tan F =
•sin F =
•cos F =
•tan F =
•sin D =
•cos D =
•tan D =
Finding Trig Ratios
Find the sine, cosine, and tangent for each
acute angle (round to 4 decimal places)
4.
5.
6.

•sin A =
•cos A =
•tan A =
•sin N =
•cos N =
•tan N =
•sin A =
•cos A =
•tan A =
•sin C =
•cos C =
•tan C =
•sin J =
•cos J =
•tan J =
•sin E =
•cos E =
•tan E =
Calculating Trig Ratios

Using a scientific calculator or the trig table to
find the following trig ratios (round to 4 decimal
places):
Angle
sin
cos
tan
Make sure
calculator is
in DEG mode
TI-83, 84, etc.
1
SIN
0
Others:
1
0
SIN
ENTER
10°
23°
30°
45°
60°
73°
89°
0.1736
0.3907
0.5000
0.7071
0.8660
0.9563
0.9998
0.9848
0.9205
0.8660
0.7071
0.5000
0.2924
0.0174
0.1763
0.4245
0.5774
1.0000
1.7321
3.2708
57.2900
sine and cosine: -1 to +1
tangent: – to +
Closure


Find the sine, cosine, and tangent of the acute angles of
the special triangles below
Write answers as radicals and approximations to 4
decimal places
C
1
B
C
45°
1
45°
A
B
60°
30°
A
Independent Practice
A calculator with
SIN, COS, and TAN
functions will be
useful!
Ch
9.5 w/s