1. I can write trig functions from a graph
Warm Up
Write the equation of the 𝒔𝒊𝒏𝒙 function with amplitude 4, shift right 𝟏𝟐𝟎°, with a period of 9 and a midline at 𝒚=𝟖
Write the equation of the graph
(𝟗𝟎,𝟒)
(𝟎,−𝟐)
(𝟏𝟖𝟎,−𝟐)

2. Warm Up
Write the equation of the 𝒔𝒊𝒏𝒙 function with amplitude 4, shift right 𝟏𝟐𝟎°, with a period of 9 and a midline at 𝒚=𝟖

3. Warm Up
Write the equation of the graph
(𝟎,−𝟐)
(𝟗𝟎,𝟒)
(𝟏𝟖𝟎,−𝟐)

4. Buffalo Problem

5. Buffalo Problem

6. A Correction…
𝑦= asin 𝑏 𝑥−ℎ +𝑘 This means… before identifying a horizontal shift, you must first factor out 𝑏.

7. A Correction…
𝑦= asin 𝑏 𝑥−ℎ +𝑘 Example: 𝑦=2 sin 3𝑥−𝜋 𝑦=2sin⁡ 3 𝑥− 𝜋 3 Shift: right 𝜋 3

8. Examples
𝑦= sin 3𝑥+180°
𝑦= cos 2𝑥−𝜋
𝑦=5cos⁡ 4𝑥+ 𝜋 2
𝑦=−sin⁡ 3𝑥−90°

9. Examples
𝑦= sin 3𝑥+180°
𝑦= cos 2𝑥−𝜋
𝒚=𝐬𝐢𝐧⁡[𝟑 𝒙+𝟔𝟎° ]
𝒚=𝒄𝒐𝒔 𝟐 𝒙− 𝝅 𝟐

10. Examples
𝑦=5cos⁡ 4𝑥+ 𝜋 2
𝑦=−sin⁡ 3𝑥−90°
𝒚=𝟓𝒄𝒐𝒔 𝟒 𝒙+ 𝝅 𝟖
𝒚=−𝒔𝒊𝒏 𝟑 𝒙−𝟑𝟎°

11. Break

12. What could we use to find x?
Trig Identity x
What could we use to find x? 3 7
Pythagorean Theorem
𝑎 2 + 𝑏 2 = 𝑐 2

13. What could we use to find x?
Trig Identity
What could we use to find x? x
𝒔𝒊𝒏(𝟔𝟎°)
𝒄𝒐𝒔(𝟔𝟎°)
𝑠𝑖𝑛 2 (60°)+ 𝑐𝑜𝑠 2 (60°)= 𝑥 2

14. Trig Identity 𝑠𝑖𝑛 2 (60°)+ 𝑐𝑜𝑠 2 (60°)= 𝑥 2 3 2 2 + 1 2 2 = 𝑥 2
= 𝑥 2
= 𝑥 2
1= 𝑥 2
𝑥=1

15. What could we use to find x?
Trig Identity
What could we use to find x? x
𝒔𝒊𝒏(𝟏𝟑𝟓°)
𝒄𝒐𝒔(𝟏𝟑𝟓°)
𝑠𝑖𝑛 2 (135°)+ 𝑐𝑜𝑠 2 (135°)= 𝑥 2

16. Trig Identity 𝑠𝑖𝑛 2 (135°)+ 𝑐𝑜𝑠 2 (135°)= 𝑥 2 2 2 2 + − 2 2 2 = 𝑥 2
− = 𝑥 2
= 𝑥 2
1= 𝑥 2
𝑥=1

17. Pythagorean Identity
𝑐𝑜𝑠 2 𝑥+ 𝑠𝑖𝑛 2 𝑥=1

18. Give your answer in positive degrees.
AA5a Problem 4
Give your answer in positive degrees.