3.09D - Solving Tangent Inequalities | High School - Edubirdie

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Trigonometry Lessons 3.09D Solving Tangent Inequalities Angles Period Solving Inequalities The process is the same Remember to visualize Visualization 1. 2. Plot the “MIDPOINT OF A CYCLE” → ℎ, 𝑘 Determine the variation 𝑂𝑅 𝑎, 𝑏 same sign 3. 𝑎, 𝑏 opposite signs Determine 2 consecutive asymptotes 𝑃 ℎ± 2 Correct interval is either: left asymptote to POI or POI to right asymptote! Example: tan(3𝑥 − 4𝜋) < −3 4 tan 3 𝑥 − 𝜋 3 < −3 −3 𝜋 𝑃= 3 7𝜋 6 𝑃 ℎ± 2 4𝜋 𝜋 = ± 3 6 4𝜋 ,0 3 3𝜋 2 tan < −3 𝐴𝑠𝑦𝑚𝑝, 𝑃𝑂𝐼 7𝜋 𝑥= 6 3𝜋 𝑥= 2 Example: tan 3 𝑥 4𝜋 θ=3 𝑥− 3 tan θ = −3 4 − 𝜋 3 < −3 𝜋 𝑃= 3 4𝜋 3 𝑥− ≈ −1.249045772 3 4𝜋 𝑥− ≈ −0.41634859 3 𝑥 ≈ 3.772441614 θ = tan−1 −3 θ ≈ −1.249045772 7𝜋 𝜋 𝜋 + 𝑛, 3.7724 + 𝑛 6 3 3 𝑤ℎ𝑒𝑟𝑒 𝑛 ∈ ℤ HW Visions 2 P118: #7cf, #8cf

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