3.08C - Graphing Transformed Sinusoidal Functions

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High School
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High School Physics
Academic year:

2024
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Trigonometry Lesson 3.08C Graphing Transformed Sinusoidal Functions Cosine Sine Cosine Function Graphing the Transformed Graphing Cosine Functions - Steps 1. 2. Sketch Sinusoidal Axis: 𝑦 = 𝑘 Choose: if 𝑎 > 0 𝑉 if 𝑎 < 0 𝑉 3. 4. Plot starting point: (ℎ, 𝑘 + 𝐴) if 𝑎 > 0 Find the Period: 𝑃= 5. 2𝜋 𝑏 Find the Amplitude: 𝐴= 𝑎 6. Divide Box for (ℎ, 𝑘 − 𝐴) if 𝑎 < 0 ℎ+ ℎ box 𝑃 4 ℎ+ 𝑃 2 𝐴 𝑦=𝑘 𝐴 key points (5 Pairs) 𝑃 ℎ+ 3𝑃 4 Graphing Cosine Functions - Steps 1. Sketch Sinusoidal Axis: 𝑉 2.1 Choose: ℎ, 𝑘 + 𝐴 𝒂>𝟎 𝑦=𝑘 if 𝑎 > 0 𝑃 2 ℎ + ,𝑘 4 point: (ℎ, 𝑘 + 𝐴) if 𝑎 > 0 3. Plot starting 𝑃 + Period: ,𝑘 − 𝐴 4.3 Findℎ the 2 2𝜋 3𝑃 1 𝑃= 4 ℎ𝑏+ ,𝑘 4 𝐴 5. Find the Amplitude: 5 ℎ + 𝑃, 𝑘 + 𝐴 𝐴= 𝑎 6. Divide Box for key points (5 Pairs) 𝑦=𝑘 if 𝑎 < 0 𝑉 (ℎ, 𝑘 − 𝐴) if 𝑎 > 0 ℎ+ 𝑃 4 ℎ+ 𝑃 2 ℎ+ 3𝑃 4 5 4 2 𝐴 3 𝑃 Graphing Cosine Functions - Steps 1. 2.1 𝒂 Sketch < 𝟎Sinusoidal Axis: 𝑦 = 𝑘 2 3. 4.3 4 5. 5 Choose: if 𝑎 > 0 ℎ, 𝑘 − 𝐴 𝑃 ℎ + ,𝑘 4 point: (ℎ, 𝑘 + 𝐴) if 𝑎 > 0 Plot starting 𝑃 Find ℎ the + Period: ,𝑘 + 𝐴 2 2𝜋 3𝑃 𝑃= ℎ𝑏+ ,𝑘 4 𝐴 Find the Amplitude: ℎ + 𝑃, 𝑘 − 𝐴 𝐴= 𝑎 6. Divide Box for key points (5 Pairs) if 𝑎 < 0 𝑉 𝑉 (ℎ, 𝑘 − 𝐴) if 𝑎 > 0 ℎ+ 𝑃 4 ℎ+ 𝑃 2 3𝑃 4 3 4 2 𝑦=𝑘 ℎ+ 𝐴 5 1 𝑃 Graph: 3 cos 1. 𝑦 = 1 2. 𝑎 > 0 𝑉 3. V (𝜋, 1 + 3) 4. P = 2 = 4 ½ 5. A = |3| = 3 6. ( , 4) (2 , 1) (3 , -2) (4 , 1) (5 , 4) 1 2 𝑥−𝜋 +1 Sine Function Graphing the Transformed Graphing Sine Functions - Steps 1. 2. 3. Sketch Sinusoidal Axis: 𝑦 = 𝑘 𝑃 4 ℎ+ 𝑃 2 Find the Vertex: (ℎ, 𝑘) and plot Find the Period: 2𝜋 𝑏 𝐴 1 𝑦=𝑘 Find the Amplitude: box 𝑃= 4. ℎ+ 𝐴 𝐴= 𝑎 5. if 𝑎, 𝑏 same 6. 𝑃 Choose: 𝑉 Divide Box for key points (5 Pairs) if 𝑎, 𝑏 diff 𝑉 ℎ+ 3𝑃 4 Graphing Sine Functions - Steps 1. Sketch Sinusoidal Axis: 𝑦 = 𝑘 2.1 Find ℎ, the 𝑘 Vertex: (ℎ, 𝑘) and plot 𝐴 3. Find the𝑃Period: 𝒂𝒃 > 𝟎 2 ℎ+ 2𝜋 𝑏 if 𝑎 > 0 6. 𝑃 4 ℎ+ 𝑃 2 ℎ+ 3𝑃 4 2 ,𝑘 + 𝐴 4 𝑃 3 ℎ + ,𝑘 4. Find the2Amplitude: 3𝑃 𝐴 = 𝑎 4 ℎ+ ,𝑘 − 𝐴 4 5. Choose: 5 ℎ + 𝑃,𝑉𝑘 𝑃= ℎ+ Divide Box for key points (5 Pairs) 𝑦=𝑘 1 3 5 𝐴 4 𝑃 if 𝑎 < 0 𝑉 Graphing Sine Functions - Steps 1. Sketch Sinusoidal Axis: 𝑦 = 𝑘 2.1 Find ℎ, the 𝑘 Vertex: (ℎ, 𝑘) and plot 𝐴 3. Find the𝑃Period: 𝒂𝒃 < 𝟎 2 ℎ+ 2𝜋 𝑏 if 𝑎 > 0 6. 𝑃 4 ℎ+ 𝑃 2 ℎ+ 3𝑃 4 4 ,𝑘 − 𝐴 4 𝑃 3 ℎ + ,𝑘 4. Find the2Amplitude: 3𝑃 𝐴 = 𝑎 4 ℎ+ ,𝑘 + 𝐴 4 5. Choose: 5 ℎ + 𝑃,𝑉𝑘 𝑃= ℎ+ Divide Box for key points (5 Pairs) 𝑦=𝑘 3 1 𝐴 2 𝑃 if 𝑎 < 0 𝑉 5 Graph: 1. Axis: 𝑦 = 1 2. V ( , 1) 3. P = 2 = 4 ½ 4. A = |3| = 3 5. a and b are + 6. ( , 1) (2 , 4) (3 , 1) (4 , -2) (5 , 1) 1 3 sin (𝑥 2 − 𝜋) + 1 HW Visions 2 Page 107: #1, #3acdf