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Trig Equations

Trig Equations . LO: Solve basic trignometric equations. Sine Function y=sinx. Cosine Function y=cosx. Tangent Function y=tanx. Review on Radians. 90 = 180 = 270 = 360 = . Sine Function. Cosine Function. Tangent Function. Vocabulary. Domain: set of possible x- values

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Trig Equations

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  1. Trig Equations LO: Solve basic trignometric equations

  2. Sine Function y=sinx

  3. Cosine Function y=cosx

  4. Tangent Function y=tanx

  5. Review on Radians • 90 = • 180 = • 270 = • 360 =

  6. Sine Function

  7. Cosine Function

  8. Tangent Function

  9. Vocabulary • Domain: set of possible x- values • Range: set of possible y- values • Period: Minimum interval of which the function repeats itself • Height of the wave function.

  10. Key Features

  11. Solving Trig Equations for

  12. for

  13. Trig Functions can also transform.. Change period + Moves left - Moves right + Moves up - Moves down Change amplitude

  14. Your turn for a b 330.2 169.8

  15. Your turn for a b 2.63 5.43

  16. How to do it using symmetry.. Solve for 0 < x 360 cos x = 0.12 x = cos 0.12 x = 83.1 or x = 360 – 83.1 x = 276.9 360 – 83.1 83.1

  17. Find x when sin x=0.46 sin x = 0.46 x = sin 0.46 x = 0.478 radians or x= – 0.478 x=2.664 rads 0.478 -0.478

  18. Rearrangements. Solve for x in the domain 2 cos x = 0.5 cos x = 0.25 [dividing each side by 2] x = cos 0.25 x = 75.5

  19. 75.5 360 - 75.5

  20. Solve for x in the domain of Solve for x in the domain 2 tan (x) + 3 = 4.5 2 tan (x) = 4.5 - 3 tan (x) = 0.75 [diving by 2] x = tan 0.75 x = 0.634

  21. 0.643 + 0.643

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