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Mastering Trigonometric Functions: Techniques and Formulas

In this comprehensive guide, we explore key strategies for solving trigonometric functions, including changing to the same function and squaring both sides using the Pythagorean Identity. Learn to set everything to one side and factor to solve equations, utilizing both double-angle and half-angle formulas. This resource includes step-by-step examples, triangle drawing strategies, and precise evaluations of angles such as sin(105°). Additionally, engage with assignments designed to enhance understanding of trigonometric equations and identities.

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Mastering Trigonometric Functions: Techniques and Formulas

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  1. ET 5.5a Solve or state where you got stuck. Two Different Trig functions: Strategy  Change to same trig function Square both sides to use Pythagorean Identity. Everything to one side = 0 Factor

  2. Double-Angle Formulas

  3. The only trig property we used to know that relates sine and cosine is Pythagorean Identity. It failed so… Solve. OH – We now know double angle formulas that relate sine and cosine. Everything to one side = 0; factor & solve.

  4. Which one does it look most like? Use a Double-Angle Formula to rewrite the equation It comes down to two choices. What are they? Why would you want to do this? Now it is in a form you know recognize and know a lot about the parent function.

  5. Evaluate Given such that Draw a triangle using given info. 5 -12 13

  6. Evaluate Given such that Start by drawing a triangle given this info. 5 -12 13

  7. 5.5 Assignments • Day 1: 3,5,7,9,11, 19, 21, 23, 25 • Day 2: 35, 41, 49, 59, 63, 75, 81, 95, 111

  8. ET 5.5b: Derive the triple angle formula • Hints: • Derive could be taken as establish. • sin3x = sin(2x + x)

  9. Copy all of the following • Pg 410: Half-Angle Formulas • Pg 411: Product-to-Sum Formulas • Pg 412: Sum-to-Product Formulas

  10. Using a half-angle formula find the exact value of sin(105°). sin(105°)= WHAT QUADRANT? + II S A T C ?

  11. Rewrite the product cos(5x)sin(4x) as a sum or difference. u v

  12. Using the sum-to-product formulas find the exact value of cos(195°) + cos(105°)

  13. Solve Solve the trig equation sin5x + sin3x = 0 Let u = 4x u 4x 4x

  14. 5.5 Assignments • Day 1: 3,5,7,9,11, 19, 21, 23, 25 • Day 2: 35, 41, 49, 59, 63, 75, 81, 95, 111

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