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)

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

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

Buffalo Problem

Buffalo Problem

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

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

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

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

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

Break

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

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

Trig Identity 𝑠𝑖𝑛 2 (60°)+ 𝑐𝑜𝑠 2 (60°)= 𝑥 2 3 2 2 + 1 2 2 = 𝑥 2 3 2 2 + 1 2 2 = 𝑥 2 3 4 + 1 4 = 𝑥 2 1= 𝑥 2 𝑥=1

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

Trig Identity 𝑠𝑖𝑛 2 (135°)+ 𝑐𝑜𝑠 2 (135°)= 𝑥 2 2 2 2 + − 2 2 2 = 𝑥 2 2 2 2 + − 2 2 2 = 𝑥 2 2 4 + 2 4 = 𝑥 2 1= 𝑥 2 𝑥=1

Pythagorean Identity 𝑐𝑜𝑠 2 𝑥+ 𝑠𝑖𝑛 2 𝑥=1

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