Sine (t3g)

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 3

Sine and cosine

April 22nd

t3d

13:15

Make some
U-shapes!

Schedule

• Starting up, programme                              5 min
• (U-shapes)
• Review:                                                               10 min
    (or: practice)
• Sine and cosine                                              15 min
• More examples & practice                        30 min
• Kahoot                                                                15 min

​A​​O​​

Programme

What do you prefer?

Inside U: more examples, practice while being 'coached'

Outside U: listen sometimes, practice

Back row: practice

Last lesson's

Intended Learning Outcomes

At the end of the lesson you could...

1. Use opposite and adjacent sides in calculations with (inverse) tangent
   

PR?

Today's

Intended Learning Outcomes

At the end of the lesson you can...

1. Calculate sides with sine and cosine
   
2. Apply the SOH CAH TOA rule

tan and tan

Want to know a side?                                        Want to know an angle?

Use tan                                                                    Use tan

                                                                                                          shift --> tan

                                                                                                           gets you tan

−1

tan(∠)=​A​​O​​

tan(​A​​O​​)=∠

−1

−1

You want to know
the length of LM.
What do you use?

1. Tangent
2. Inverse tangent
3. Sine
4. There's not enough information

Calculate the length of LM.
Round to the nearest tenth.

1. 10.9
2. 16.3
3. 19.4
4. 20.6

sin and sin       

Want to know a side?                                         Want to know an angle?

Use sin                                                                      Use sin

−1

−1

sin(∠)=​H​​O​​

sin(​H​​O​​)=∠

−1

Chapter 7

Basic route 

37, 38, 44, 45, 47, 48, 52

Advanced route

38, 40, 42, 48, 49, 51

cos and cos      

Want to know a side?                                         Want to know an angle?

Use cos                                                                     Use cos

−1

−1

cos(∠)=​H​​A​​

cos(​H​​A​​)=∠

−1

Chapter 7

Basic route 

37, 38, 44, 45, 47, 48, 52

Advanced route

38, 40, 42, 48, 49, 51

Cosine

                                           Example: calculate BC.

−1

cos(∠)=​H​​A​​

cos(​H​​A​​)=∠

Basic route 

37, 38, 44, 45, 47, 48, 52

Advanced route

38, 40, 42, 48, 49, 51

Cosine

                                         Example: calculate          .

−1

cos(∠)=​H​​A​​

cos(​H​​A​​)=∠

∠B

Basic route 

37, 38, 44, 45, 47, 48, 52

Advanced route

38, 40, 42, 48, 49, 51

Trigonometric ratios         

How to remember

SOH

CAH

TOA

                                                                                         

Basic route 

37, 38, 44, 45, 47, 48, 52

Advanced route

38, 40, 42, 48, 49, 51

Trigonometric ratios              

How to remember

SOH

CAH

TOA

                                                                                         

cos(∠)=​H​​A​​

sin(∠)=​H​​O​​

tan(∠)=​A​​O​​

Basic route 

37, 38, 44, 45, 47, 48, 52

Advanced route

38, 40, 42, 48, 49, 51

Trigonometric ratios          

Want to know a side?                                        Want to know an angle?

Use sin/cos/tan                                                   Use sin   /cos   /tan

                                                                                       calculator:

                                                                                      shift --> sin/cos/tan

                                                                                         

−1

−1

−1

Basic route 

37, 38, 44, 45, 47, 48, 52

Advanced route

38, 40, 42, 48, 49, 51

You want to know
the length of KM.
What do you use?

1. Tangent
2. Sine
3. Inverse sine
4. Inverse cosine

You want to know
the size of
What do you use?

∠C.

1. Tangent
2. Sine
3. Inverse sine
4. Inverse cosine

You want to know
the length of LM.
What do you use?

1. Inverse sine
2. Inverse cosine
3. Tangent
4. Cosine

Calculate KM.
Round to the
nearest integer.

1. 3
2. 4
3. 6
4. 7

Calculate LM.
Round to the
nearest integer.

1. 3
2. 4
3. 6
4. 7

Chapter 7

Basic route 

37, 38, 44, 45, 47, 48, 52

Advanced route

38, 40, 42, 48, 49, 51

Practice

Chapter 7

Basic route 

37, 38, 44, 45, 47, 48, 52

Advanced route

38, 40, 42, 48, 49, 51

Kahoot!