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Trigonometry Challenge: Solve Equations and Simplify Expressions

Demonstrate understanding of multiple angle formulas in trigonometry by solving equations and simplifying expressions. Practice rewriting trigonometric functions in terms of basic functions for x in [0, 2π]. Test your skills with challenges on sin(3x) and cos(3x) formulas.

sherryrodriguez
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Trigonometry Challenge: Solve Equations and Simplify Expressions

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  1. Multiple Angle FormulasES: Demonstrating understanding of concepts Warm-Up: Use a sum formula to rewrite sin(2x) in terms of just sin(x) & cos(x). Do the same for cos(2x). Now rewrite tan(2x) in terms of tan(x). .

  2. Solve the Equation for x in [0, 2π) • sin(2x) = 0

  3. Solve the Equation for x in [0, 2π) 2) sin(2x)sinx = cos(x)

  4. Simplify the expression. 4sin(3x)cos(3x)

  5. Simplify the expression. 3cos2(2x) – 3sin2(2x)

  6. Simplify the expression. 2sin3(x)cos(x) – 2sin(x)cos3(x)

  7. Verify

  8. I propose a challenge to you.Test your trig manipulation skills and try to find formulas for sin(3x) in terms of sin(x) & cos(3x) in terms of cos(x). As a second challenge, how do you know if your answer is correct or not???

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