Transcript Trigonometric Functions of Angles

Trigonometric Functions
Chapter 4
4.1 Right Triangle
Trigonometry
- Finding the six trigonometric ratios.
- Solving right triangles.
- Using a calculator to find trig ratios.
Trigonometric Ratios: ratios of
sides of a right triangle.
θ
hyp
hyp
opp
adj
θ
adj
opp
Θ is an acute angle!!!!!!
6 Trigonometric Ratios:
3 basic:
opp
sin  
hyp
adj
cos  
hyp
opp
tan  
adj
3 additional:
hyp
csc  
opp
hyp
sec  
adj
adj
cot  
opp
Since any two right triangles with angle θ
are similar, these ratios are the same,
regardless of the size of the triangle.
50
30
5
3
θ
4
θ
40
You try…
Find the values of the 6 trig ratios of
angle θ:
7
θ
3
2 10
12
If tan   , find the other 5 trig ratios.
5
Solving Right Triangles: determine 3
side lengths and 3 angle measures.
Must give you three out of 6 parts.
A
c
b
C
a
Angles
A=
B=
C=
Sides
a=
b=
c=
+ 180°
Pythag Th
B
CHECK MODE OF CALCULATORS!
Solve the Right Triangle
Angles
A = 42°
B=
C=
A
c
b
C
a
B
Sides
a=
b=
c=4
Solve the Right Triangle
Angles
A=
B=
C=
A
c
b
C
a
B
Sides
a=3
b=
c = 14
Applications:
- Line of sight: line from observer’s eye to
object
- Angle of elevation: object is above
horizontal, angle between line
of sight and horizontal
- Angle of depression: object is below
horizontal, angle between line
of sight and horizontal
Example
A person standing 100 feet from the bottom
of a cliff notices a tower on top of the cliff.
The angle of elevation to the top of the cliff
is 30°, and the angle of elevation to the top
of the tower is 58°. How tall is the tower?
Checkpoint.
You are standing on top of a vertical cliff 40
meters high. You see your car parked away
from the base of the cliff. The angle of
depression that your car makes with the cliff
is 34º. How far is the car from the base of
the cliff?
4.1 Homework
p. 227 #6, 12, 18, 22, 34, 42, 56, 57 – 67 odd
p. 52 #25, 35, 66, 67