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Comprehensive Trigonometry Review: Solving Trig Equations, Graphs, and Triangle Applications

This comprehensive review focuses on solving various trigonometric equations, determining angles, and analyzing trigonometric functions over defined intervals. Key topics include solving sine and cosine equations within specified ranges, understanding domain, range, and period of functions, and finding angles based on given ratios. Additionally, it covers calculations in right triangles and values of six trigonometric functions. Students are encouraged to memorize key concepts and methods to enhance recall and understanding, aiding their success in trigonometry.

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Comprehensive Trigonometry Review: Solving Trig Equations, Graphs, and Triangle Applications

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  1. 6.1 – 6.5 Review!! Examples  Graph the following: Solve for the following: sin x = 0.32 on [0, 2π) cosx = -0.75 on [-π, π] sin x = -0.14 cosx = 0.65 • y = 4sin x • y = -3cos (2x) • y = sin (0.5x) + 1 • y = 2sin (x – 1)

  2. 6.1 – 6.5 Review!! Test Review!! Solve each over a single period, then state the domain, range and period. • Solve the following on the given interval:

  3. 6.1 – 6.5 Review!! Determining Ɵ • Given the following, find the measure of Ɵ in both degrees and radians.

  4. 6.1 – 6.5 Review!! Examples: Find all angles on the given interval with the same trig ratio. • Prove the following:

  5. 6.1 – 6.5 Review!! Even More Examples!! Find the values of the six trig functions and determine the angles of measure from P(5, -2). • Solve the following right triangle: <A = 20°, a = 12.3 • Find all the trig values when Ɵ = 65° in standard position on the unit circle.

  6. 6.1 – 6.5 Review!! P.S. – Advice!! Solve 1 variable = find that variable Solve 2 variable = graph! All triangles add up to 180° • KNOW YOUR MEMORIZATION QUIZZES!! • Know rotations • Know each graph and it’s basic info

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