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5.3 Solving Trig Equations(day2)

Learn how to solve trigonometric equations using factoring. Avoid common mistakes and find angle measures in various quadrants. Includes examples and homework.

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5.3 Solving Trig Equations(day2)

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  1. 5.3 Solving Trig Equations(day2)

  2. 5.3 Solving Trig Equations Objectives: • Use factoring to solve complicated trig equations

  3. WARm-up • Factor: x4 – 5x2 + 6 • Factor: x3 + 5x2 + 3x + 5 • Solve by factoring: 4x2 = 5x • Solve by factoring: 3x2 – 11x – 4 = 0

  4. 5.3 Solving Trig Equations WARNING!!!!! • Do not divide by sin, cos, tan, sec, csc or cot! You may lose answers. • Always check your solutions

  5. Type #2: Example 1: Solve by Factoring On the interval [0, 360) 1. Set equal to zero and factor to solve. 2. Determine the quadrants: tan positive first and third

  6. Ex 2: Solve by Factoring 1. Set equal to zero and factor to solve 2. Determine the quadrants + and -, All quadrants 3. Find the angle measure

  7. Ex 3: Solve by Factoring SOLVE: cos4 x + cos2 x = 2 1. Set equal to zero and factor to solve cos4 x + cos2 x – 2 = 0 (cos2 x + 2)(cos2 x – 1) = 0 cos2 x + 2 = 0 cos2 x – 1 = 0 cos2 x = -2 cos2 x = 1 Ø 2. Find the angle measure

  8. Ex4: Solve by Factoring SOLVE: 8sin3 x + 4sin2 x – 6sin x = 3 1. Set equal to zero and factor to solve 8sin3x + 4sin2x – 6sin x – 3 = 0 4sin2x(2sinx + 1) – 3(2sinx + 1) = 0 (4sin2x – 3)(2sinx + 1) = 0 2. Find the angle measure X = 60°, 120°,240°,300° 210°, 330°

  9. Homework: 5.3 Day 2 Worksheet

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