Section 5.2 Right Triangle Trigonometry
Function Values for Some Special Angles
Example
0 0 0Find the csc 30 , sec 30 , cot 30
30-60-90 & 45-45-90
Right Triangle Definitions of Trigonometric Functions
Oscar Has A Heap Of Apples
Trigonometry values for a given angle are always the same no matter how large the
triangle is
Example
Find the value of each of the six trigonometric functions
of if b=4 and c=2 5.
4b
2 5c
• Find the exact values of the 6 trig functions for the following…
Find the exact values of the 6 trig functions for the following…
Find the other 5 trig functions if…
7
5cos
• Find the other 5 trig functions if…
5cot
• Find…
– cos60°– csc30°– tan60°
• Find the other 5 trig functions if…
4
17csc
• Find…
sin45°cos30°tan30°
Trigonometric Functions and Complements
Example
Find a cofunction with the same value as the given expression:
cos 20
cot 40
o
o
An angle formed by a horizontal line and the line
of sight to an object that is above the horizontal
line is called the angle of elevation. The angle formed
by a horizontal line and the line of sight to an object
that is below the horizontal line is called the angle of
depression. Transits and sextants are instruments
used to measure such angles.
Example
The irregular blue shape is a pond. The distance across
the pond, a, is unknown. To find this distance, a
surveyor took the measurements shown in the figure.
What is the distance across the pond?
1200 yards
The inverse function for tangent and the other angles
can be accessed on your calculator the same way.
Example
36 feet
40 feet
A building is 40 feet high and it casts a shadow
36 feet long. Find the angle of elevation of the
sun to the nearest degree.
(a)
(b)
(c)
(d)
3
1Find the cos .
3 10
103
10
10
101
10
(a)
(b)
(c)
(d)
30o
50 feet
0
Find the height of the tree if the length of the
shadow is 50 feet when the sun is at a 30 angle.
25 feet
25.56 feet
28.87 feet
30 feet
Exit Slip1) Find the six trig functions of the angle…
4
8
A B
C
• Find the…
2) tanθ 3) cos θ
3
1sin 4csc
Find the six trig functions if…
4) cos θ 5) sin θ
3sec 7
9tan