Transcript CLASS 1 CHARACTERISTICS of FUNCTIONS, ALGEBRAICALLY

Chapter 6 – Trigonometric Functions:
Right Triangle Approach
6.2 - Trigonometry of Right Triangles
Definitions

In this section, we will study certain ratios of sides of
right triangles, called trigonometric rations, and
discuss several applications.
6.2 - Trigonometry of Right Triangles
Trigonometric Ratios

Consider a right triangle with  as one of its acute
angles. The trigonometric ratios are as follows:
sin  
opposite
hypotenuse
cos  
adjacent
hypotenuse
tan  
opposite
adjacent
csc  
hypotenuse
opposite
sec  
hypotenuse
adjacent
cot  
adjacent
opposite
6.2 - Trigonometry of Right Triangles
Examples – pg. 448

Find the exact value of the six trigonometric ratios of
the angle  in the triangle.
6.2 - Trigonometry of Right Triangles
Examples – pg. 448

Find the side labeled x. State your answer rounded to
five decimal places.
6.2 - Trigonometry of Right Triangles
Examples – pg. 448

Find the side labeled x. State your answer rounded to
five decimal places.
6.2 - Trigonometry of Right Triangles
Special Triangles
30 or


6
, 45 or

4
, 60 or

3
First we will create an isosceles right triangle.
Find the ratio of the sides for all 6 trig functions.
2
1
45
1
6.2 - Trigonometry of Right Triangles
Special Triangles
30 or


6
, 45 or

4
, 60 or

3
Next we will create an equilateral triangle. Find the
ratio of the sides for all 6 trig functions.
30
60
1
1
6.2 - Trigonometry of Right Triangles
Special Triangles
 in
 in
degrees radians
sin
cos
tan
csc
sec
2
2 3
3
30o

6
1
2
3
2
3
3
45o

4
2
2
2
2
1
60o

3
3
2
1
2
3
6.2 - Trigonometry of Right Triangles
2
2 3
3
cot
3
2
1
2
3
3
Examples – pg. 449

Solve the right triangle.
6.2 - Trigonometry of Right Triangles
Applications

The ability to solve right triangles by using
trigonometric ratios is fundamental to many problems
in navigation, surveying, astronomy, and the
measurement of distances.

We need to have common terminology.
6.2 - Trigonometry of Right Triangles
Definitions

Line of Sight
If an observer is looking at an object, then the line
from the eye of the observer to the object is called
the line of sight.
6.2 - Trigonometry of Right Triangles
Definitions

Angle of Elevation
If the object being observed is above the horizontal
(plane) then the angle between the line of sight and
the object is called the angle of elevation.
6.2 - Trigonometry of Right Triangles
Definitions

Angle of Depression
If the object being observed is below the horizontal
(car) then the angle between the line of sight and the
object is called the angle of depression.
6.2 - Trigonometry of Right Triangles
NOTE

Angle of Inclination
In many of the examples, angles of elevation and
depression will be given for a hypothetical observer
at ground level. If the line of sight follows a physical
object, such as a plane or hillside, we use the term
angle of inclination.
6.2 - Trigonometry of Right Triangles
Examples – pg. 450
6.2 - Trigonometry of Right Triangles
Examples – pg. 450
6.2 - Trigonometry of Right Triangles
Examples – pg. 450
6.2 - Trigonometry of Right Triangles
Examples – pg. 450
6.2 - Trigonometry of Right Triangles
Examples – pg. 450
6.2 - Trigonometry of Right Triangles