Math 1316
Section 6.2 6.3 Class Notes
Trigonometric Equations
Solving Equations by Linear Methods
Example 1: (page 278) Solve each equation over the interval [0, 2π).
13. 2sin x + 3 = 4
14. 2sec x + 1 = sec x + 3
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Math 1316
17. (
Section 6.2 6.3 Class Notes
)(√
)
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Math 1316
Section 6.2 6.3 Class Notes
Example 2: Solve each equation over the interval [0o, 360o).
23. (
√ )(
√ )
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Math 1316
Section 6.2 6.3 Class Notes
12. sin x + 2 = 3
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Math 1316
Section 6.2 6.3 Class Notes
Solving Equations by Factoring
Example 3: Solve each equation over the interval [0, 2π). Give solutions to the nearest
tenth as appropriate.
19. cos2 x + 2 cos x + 1 = 0
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Math 1316
20.
Section 6.2 6.3 Class Notes
√
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Math 1316
Section 6.2 6.3 Class Notes
22. 2cos2 x – cos x = 1
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Math 1316
Section 6.2 6.3 Class Notes
Example 4: Solve each equation over the interval [0o, 360o). Give solutions to the nearest
tenth as appropriate.
25. 2sin θ – 1 = csc θ
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Math 1316
Section 6.2 6.3 Class Notes
30. sin2 θ cos θ = cos θ
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Math 1316
Section 6.2 6.3 Class Notes
33. sec2 θ tan θ = 2tan θ
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Math 1316
Section 6.2 6.3 Class Notes
34. cos2 θ – sin2 θ = 0
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Math 1316
Section 6.2 6.3 Class Notes
39. sin2 x – 2sin x + 3 = 0
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Math 1316
Section 6.2 6.3 Class Notes
42. 2sin θ = 1 – 2cos θ
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Math 1316
Section 6.2 6.3 Class Notes
Example 5: (page 284) Solve each equation over the interval [0, 2π).
7.
√
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Math 1316
Section 6.2 6.3 Class Notes
17. sin x = sin 2x
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Math 1316
Section 6.2 6.3 Class Notes
28.
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Math 1316
Section 6.2 6.3 Class Notes
40. sin θ – sin 2θ = 0
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