Transcript Sec 6.2 Trigonometry of Right Triangles

Sec 6.2
Trigonometry of Right Triangles
Objectives:
•To define and use the six trigonometric
functions as ratios of sides of right
triangles.
•To review special right triangles.
•To solve right triangles using
trigonometric ratios.
Trigonometric Ratios
opposite
adjacent
opposite
sin  
cos  
tan  
hypotenuse
hypotenuse
adjacent
hypotenuse
hypotenuse
adjacent
csc  
sec  
cot  
opposite
adjacent
opposite
Ex 1. Find the six trig ratios of the angle .
Ex 2. Sketch a right triangle with acute angle  and find
the other five trig ratios of .
a)
3
cos  
4
b)
13
csc  
12
Class Work
1. Find the six trig ratios of the angle .
7

6
2. a) Find sin  and cos 

b) Find tan  and cot 
c) Find sec  and csc 
4
7

3. Sketch a right triangle with acute angle  and
find the other five trig ratios of .
7
a) cos  
8
b) tan   3
Special Triangles
45
2
30
1
3
45
60
1
1
 in
 in
degrees
radians
30
45
60
sin 
cos 
2
tan 
csc 
sec 
cot 
Ex 3. Evaluate the following without a calculator.
a) sin

3
 cos

3
b) cos60 sec60
Ex 4. Find the exact value of x.
60
x
a)
x
13
45
b)
21
Class Work
Evaluate the expression without using a calculator.
4. sin 30 csc 30



 
5.  sin cos  sin cos 
3
6
6
3

2
Find the exact value of x.
6.
7.
Solving a Right Triangle
• A triangle has six parts—three angles and
three sides.
• To solve a triangle means to determine all
of its parts from the information known about
the triangle.
– In other words, we determine the lengths
of the three sides and the measures of
the three angles.
Ex 5. Solve the triangle.
a)
b)
Class Work
Solve the triangle.
8.
9.
10. From the top of a 200 ft lighthouse, the angle of
depression to a ship in the ocean is 23. How far is
the ship from the base of the lighthouse?
HW #2 p484 1-35 odd,
49, 50.