1. Warm – up #4
1. Find the exact value of 2 𝑐𝑜𝑠 2 𝜋 4 − − −1 1 – 1 = 0

2. Homework Log Fri 3/11 Lesson 7 – 8 Learning Objective:
To graph sine & cosine
Hw: #720 Pg. 452 #1 – 4 all,
13 – 20 all

3. 3/11/16 Lesson 7 – 8 Sinusoidal Graph
Advanced Math/Trig

4. Learning Objective
To graph sine & cosine

5. Graph of y = sinx Period = 2𝜋 Amplitude = 𝑚𝑎𝑥−𝑚𝑖𝑛 2 = 1−(−1) 2 =1 x y
1 2
2 2 ≈0.7
3 2 ≈0.87 1
– 1
𝜋 6
𝜋 4
𝜋 3
𝜋 2
𝜋 3𝜋 2 2𝜋 1 –1
Period = 2𝜋
Amplitude = 𝑚𝑎𝑥−𝑚𝑖𝑛 2 = 1−(−1) 2 =1

6. General Sine Curve 𝑦= asin 𝑏 𝑥−𝑐 +𝑑 Amp = 𝑎 Period = 2𝜋 𝑏
We’ll do c & d tomorrow
Period = 2𝜋 𝑏
If a is (+), typical sine curve
If a is (–), reflect through x–axis

7. 1. Graph y = 3sinx 𝑦= asin 𝑏 𝑥−𝑐 +𝑑 b = 1 c = 0 a = 3 d Amp = 3
𝜋 2 𝜋
3𝜋 2 2𝜋 –3
Amp = 3
Period = 2𝜋
Increment length
= Period∙ 1 4
= 2π∙ 1 4
= 𝜋 2

8. 2. Graph y = sin2x 𝑦= asin 𝑏 𝑥−𝑐 +𝑑 b = 2 c = 0 a = 1 d Amp = 1 Per:
𝜋 4
𝜋 2
3𝜋 4 𝜋 –1
Amp = 1
Per:
IL:
= 2𝜋 𝑏
= 2𝜋 2
= 𝜋
= Period∙ 1 4
= π∙ 1 4
= 𝜋 4

9. 3. Graph y = 2sin3x 𝑦= asin 𝑏 𝑥−𝑐 +𝑑 b = 3 c = 0 a = 2 d Amp = 2 Per:
𝜋 6
𝜋 3
𝜋 2
2𝜋 3 –2
Amp = 2
Per:
IL:
= 2𝜋 𝑏
= 2𝜋 3
= Period∙ 1 4
= 2𝜋 3 ∙ 1 4
= 𝜋 6

10. 4. Graph y = –sin4x 𝑦= asin 𝑏 𝑥−𝑐 +𝑑 b = 4 c = 0 a = –1 d Amp = 1 Per:
𝜋 8
𝜋 4
3𝜋 8
𝜋 2 –1
Amp = 1
Per:
IL:
= 2𝜋 𝑏
= 2𝜋 4
= 𝜋 2
a = (–) so reflect over x – axis!
= Period∙ 1 4
= 𝜋 2 ∙ 1 4
= 𝜋 8

11. 5. Graph y = –3sinx 𝑦= asin 𝑏 𝑥−𝑐 +𝑑 b = 1 c = 0 a = –3 d Amp = 3 Per:
𝜋 2 𝜋
3𝜋 2 2𝜋 –3
Amp = 3
Per:
IL:
= 2𝜋 𝑏
= 2𝜋 1
= 2𝜋
a = (–) so reflect over x – axis!
= Period∙ 1 4
= 2𝜋∙ 1 4
= 𝜋 2

12. Graph of y = cosx Period = 2𝜋 Amplitude = 𝑚𝑎𝑥−𝑚𝑖𝑛 2 = 1−(−1) 2 =1 x y
3 2 ≈0.87
2 2 ≈0.7
1 2
– 1
𝜋 6
𝜋 4
𝜋 3
𝜋 2
𝜋 3𝜋 2 2𝜋 1 –1
Period = 2𝜋
Amplitude = 𝑚𝑎𝑥−𝑚𝑖𝑛 2 = 1−(−1) 2 =1

13. General Cosine Curve 𝑦= a𝑐𝑜𝑠 𝑏 𝑥−𝑐 +𝑑 Amp = 𝑎 Period = 2𝜋 𝑏
We’ll do c & d tomorrow
Period = 2𝜋 𝑏
If a is (+), typical cosine curve
If a is (–), reflect through x–axis

14. 6. Graph y= 1 3 cos(2𝑥) 𝑦= a𝑐𝑜𝑠 𝑏 𝑥−𝑐 +𝑑 = 2 b = 0 c = 1/3 a d
𝜋 4
𝜋 2
3𝜋 4 𝜋
− 1 3
Amp = 1/3
Per:
IL:
= 2𝜋 𝑏
= 2𝜋 2
= 𝜋
= Period∙ 1 4
= π∙ 1 4
= 𝜋 4

15. 7. Graph y=2cos(5𝑥) 𝑦= a𝑐𝑜𝑠 𝑏 𝑥−𝑐 +𝑑 = 5 b = 0 c = 2 a d Amp = 2 Per:
𝜋 10
𝜋 5
3𝜋 10
2𝜋 5 −2
Amp = 2
Per:
IL:
= 2𝜋 𝑏
= 2𝜋 5
= Period∙ 1 4
= 2𝜋 5 ∙ 1 4
= 𝜋 10

16. 8. Graph y=−2cos( 1 2 𝑥) 𝑦= a𝑐𝑜𝑠 𝑏 𝑥−𝑐 +𝑑 = 1/2 b = 0 c = –2 a d𝜋 2𝜋 3𝜋 4𝜋
Amp = 2
Per:
IL: –2
= 2𝜋 𝑏
= 2𝜋 1/2
= 4𝜋
a = (–) so reflect over x – axis!
= Period∙ 1 4
= 4π∙ 1 4
= 𝜋

17. 9. Graph y=− 1 4 cos( 𝑥 5 ) 𝑦= a𝑐𝑜𝑠 𝑏 𝑥−𝑐 +𝑑 = 1/5 b = 0 c = –1/4 a d
5𝜋 2 5𝜋
15𝜋 2
10𝜋
Amp = 1 4
Per:
IL:
− 1 4
= 2𝜋 𝑏
= 2𝜋 1/5
= 10𝜋
a = (–) so reflect over x – axis!
= Period∙ 1 4
= 10π∙ 1 4
= 5𝜋 2

18. Ticket Out the Door
Graph y = – cos 𝑥 4

19. Homework
#720 Pg. 452 #1 – 4 all, 13 – 20 all