3.09C - Solving Tangent Equations | High School - Edubirdie

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Trigonometry Lessons 3.09C Solving Tangent Equations Angles Period Steps for Solving 1. Identify Period 𝑃 = 2. Set to zero 3. 4. 5. 6. 7. Isolate tan 𝑏 𝑥 − ℎ 𝜋 𝑏 Let θ = 𝑏 𝑥 − ℎ Solve θ (unit circle, or calculator (tan−1 Solve for 𝑥 using Generalize 𝜃 =𝑏 𝑥−ℎ 𝑥 + 𝑃𝑛 𝑤ℎ𝑒𝑟𝑒 𝑛 ∈ ℤ )) Example: 0 = tan 3 𝑥 − 𝜋 1 = tan 3 𝑥 − 𝜋 θ=3 𝑥−𝜋 1 = tan(θ) 𝜋 𝜃= 4 −1 𝜋 𝑃= 3 𝜋 =3 𝑥−𝜋 4 13𝜋 =𝑥 12 13𝜋 𝜋 + 𝑛 𝑤ℎ𝑒𝑟𝑒 𝑛 ∈ ℤ 12 3 Example: 𝑓 𝑥 = 3tan 2 𝜋 0 = 3tan 𝑥− 3 4 3 2 𝜋 = tan 𝑥− 3 3 4 2 𝜋 θ= 𝑥− 3 4 3 = tan(θ) 3 𝜋 𝜃= 6 − 3 2 3 𝑥− 𝜋 4 − 3 3𝜋 𝑃= 2 𝜋 2 𝜋 = 𝑥− 6 3 4 𝜋 =𝑥 2 𝜋 3𝜋 + 𝑛 𝑤ℎ𝑒𝑟𝑒 𝑛 ∈ ℤ 2 2 Example 1: 2 tan 1 3 tan 𝑥− 𝜋 3 2 1 3 θ= 𝑥− 𝜋 3 2 tan θ = −3 θ = tan−1 (−3) 1 3 𝑥− 3 𝜋 2 = −6 𝜋 𝑃= = 3𝜋 1 3 θ ≈ −1.249045772 = −3 1 3 𝑥 − 𝜋 = −1.249045772 3 2 𝑥 = 0.965251663 0.9653 + 3𝜋𝑛 𝑤ℎ𝑒𝑟𝑒 𝑛 ∈ ℤ HW Visions 2 P118: #1cf, #2cf, #4cf

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