Section 5.2 Right Triangle Trigonometry. Function Values for Some Special Angles.

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

Applications

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