Download sine and cosine ratios

Lesson 5.3
Apply the Sine and Cosine Ratios.
Georgia Performance Standards:
MM2G2a, MM2G2b, MM2G2c
B
Vocabulary
A
C
• The sine and cosine ratios are trigonometric
ratios for acute angles that involve the lengths
of a leg and the hypotenuse of a right triangle.
• Let ∆ ABC be a right triangle with acute A.
The sine of A and cosine of A (written as
sin A and cos A) are defined as follows:
opposite
sin A 
hypotenuse
adjacent
cos A 
hypotenuse
SOH-CAH-TOA
SOH
CAH
TOA
sin A 
cos A 
tan A 
opposite
BC

hypotenuse AB
adjacent
AC

hypotenuse AB
opposite BC

adjacent AC
B
A
C
SOH-CAH-TOA
• The Legend of Soh-Cah-Toa
Mental Princess of the Ages
– http://www.themathlab.com/writings/short%20
stories/sohcahtoa/overview.htm
• Studying Our Homework -Can Always Help - To
Obtain Achievement."
Example 1 Find sin X and sin Y. Write each
answer as a fraction and as a decimal rounded to
four places.
sin X 
sin Y 
20
52
48
52
 0.3846153846
 0.3846
 0.9230769231
 0.9231
SOH
sin
opposite
A
hypotenuse
Example 2 Find cos X and cos Y. Write each
answer as a fraction and as a decimal rounded to
four places.
cos X 
cos Y
48
52
 0.9230769231
 0.9231
20  0.3846153846

52
 0.3846
sin X 
sin Y 
20
52
48
52
 0.3846153846
 0.3846
 0.9230769231
 0.9231
Aren't these the
same answers we
just had for sin?
CAH
adjacent
cos A 
hypotenuse
Example 4a Use a trigonometric ratio to find the value
of x in the diagram. Round to the nearest tenth.
Decide what you have in
terms of opposite,
adjacent, hypotenuse.
cos 29 

adjacent
hypotenuse
Which of the three is
missing?
18
cos 29 
x

C
a
h
CAH
Solve for x
Example 4b Use a trigonometric ratio to
find the value of x in the diagram. Round to
the nearest tenth.
Decide what you have in
terms of opposite,
adjacent, hypotenuse.
sin 42 
S
o
h
opposite
hypotenuse
SOH
Which of the three is
missing?
x

sin 42 
52
Solve for x
Homework 1 – 3, 7 – 9 page 166
Homework 15, 16, 17 21, and 22
page 167