GeometryTrigonometry

Learning Outcomes

• I will be able to set up all trigonometric ratios for a right triangle.

• I will be able to set up all trigonometric ratios for a right triangle

Reminder: Unit Circle

WRITE THIS DOWN!

•SOH CAH TOA

Vocabulary

• θ – greek letter theta – this symbol is used to represent angle measures.• Sine – is the ratio of the length of the side opposite the angle and the hypotenuse.• Cosine - is the ratio of the length of the side adjacent to the angle and the hypotenuse.• Tangent – is the ratio of the length of the side

opposite the angle and the side adjacent to the angle.

What do we know?

• The triangles are similar.• The angles are congruent.

3

56

10

What do we know?

• The triangles are similar.• The angles are congruent.

5

12

10

24

What do we know?

• The triangles are similar.• The angles are congruent.

24

25 50

48

Why is this important?

• What happens if I know one angle measure for one of these triangles? (Other than the 90° angle?)

• I can find all the others in that triangle and for any similar triangle.

3

56

10

Trigonometric Functions

• This is why we created sine, cosine and tangent. Before we can use Sine, Cosine and Tangent we have to understand how to label our triangles.

θOpp

osit

e Hypotenuse

Adjacent

Try these on your own

• Correctly label the sides

θOpp

osit

e

Hypotenuse

Adjacent

θOpposite

Hypotenuse

Adj

acen

t

Activity

• You have a card and must find your partner.

20

21

29

θ20

21

29θ

20

21

29O

A

H

20

21

29

O

A

H

Remember This?

• SOH CAH TOA

• Sine =

• Cosine =

• Tangent =

What do we know?

• Just by looking at this triangle what do we know about it?

2

4

2

A

B C

Using Trigonometry

• What is the sin A?• sin A = or • What is the cos A?• cos A = or • What is the tan A?• tan A = or

2

4

2

A

B C

Using Trigonometry

• What is the sin A?• sin A = or • What is the cos A?• cos A = or • What is the tan A?• tan A = or

24

48

2

A

B C

Take out your calculators

• Find the sin function on your calculator, then plug in sin 60.

• You should get .8660254038

• Remember we said the sin A = or . Plug this into your calculator.

• You should get .8660254038

24

2

A

B C

60°

30°

Try this on your own

sin A = cos A =

tan A =

sin A = cos A =

tan A =

sin A = cos A =

tan A =

Try this on your own

Exit Ticket Homework

• Find the sine, cosine and tangent of B. Give the exact and approximate answer.

• Pg. 562: 10-27