1 / 16

Solving Trig Equations

End. 1 step problems : solutions A B 2 step problems : solutions A B C 3 step problems : solutions A B C Multiple solutions : solutions A B Overview: Trig Equations. Solving Trig Equations. A. A. A. A. A. S. S. S. S. S. 0, 360. 0, 360. 0, 360. 0, 360. 0, 360. 180. 180.

ornice
Télécharger la présentation

Solving Trig Equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. End 1 step problems: solutions AB 2 step problems: solutions ABC 3 step problems: solutions ABC Multiple solutions: solutions AB Overview: Trig Equations Solving Trig Equations

  2. A A A A A S S S S S 0, 360 0, 360 0, 360 0, 360 0, 360 180 180 180 180 180 T T T T T C C C C C Home End 1 step problems Solving Trig Equations (A) (all in degrees, 0 ≤ x ≤ 360) 1) Solve Sin X = 0.24 2) Solve Cos X = 0.44 3) Solve Tan X = 0.84 4) Solve Sin X = -0.34 5) Solve Cos X = -0.77

  3. A A A S S S 0, 360 0, 360 0, 360 180 180 180 T T T C C C Home End 1 step solns A 1) Solve Sin x = 0.24 Positive Sin so quadrant 1 & 2 x = Sin-1 0.24 1st solution: x = 13.9° 2nd solution: x = 180 – 13.9 = 166.1° Positive Cos so quadrant 1 & 4 2) Solve Cos X = 0.44 x = Cos-1 0.44 1st solution: x = 63.9° 2nd solution: x = 360 – 63.9 = 296.1° 3) Solve Tan X = 0.84 Positive Tan so quadrant 1 & 3 x = Tan-1 0.84 1st solution: x = 40.0° 2nd solution: x = 180 + 40.0 = 220.0°

  4. A A S S 0, 360 0, 360 180 180 T T C C Home End 1 step solns B 4) Solve Sin x = -0.34 Negative Sin so quadrant 3 & 4 x = Sin-1 0.34 = 19.9º Use positive value 1st solution: x = 180 + 19.9° = 199.9º 2nd solution: x = 360 – 19.9 = 340.1° 5) Solve Cos x = -0.77 Negative Cos so quadrant 2 & 3 x = Cos-1 0.77 = 39.6º Use positive value 1st solution: x = 180 – 39.6° = 140.4º 2nd solution: x = 180 + 39.6 = 219.6°

  5. A A A A A S S S S S 0, 360 0, 360 0, 360 0, 360 0, 360 180 180 180 180 180 T T T T T C C C C C Home End 2 step problems 1) Solve 4Sin x = 2.6 2) Solve Cos x + 3 = 3.28 3) Solve 2Tan x + 2 = 5.34 4) Solve 2 + Sin x = 1.85 5) Solve 0.5Cos x + 3 = 2.6

  6. A A S S 0, 360 0, 360 180 180 T T C C Home End 2 step solutions A 1) Solve 4Sin x = 2.6 Positive Sin so quadrant 1 & 2 Sin x = 0.65 Divide by 4 x = Sin-1 0.65 = 40.5º 1st solution: x = 40.5º 2nd solution: x = 180 – 40.5 = 139.5° 2) Solve Cos x + 3 = 3.28 Positive Cos so quadrant 1 & 4 Cos x = 0.28 Subtract 3 x = Cos-1 0.28 = 73.7º 1st solution: x = 73.7º 2nd solution: x = 360 – 73.7 = 286.3°

  7. A A S S 0, 360 0, 360 180 180 T T C C Home End 2 step solutions B 3) Solve 2Tan x + 2 = 5.34 Positive Tan so quadrant 1 & 3 Subtract 2 2Tan x = 3.34 Divide by 2 Tan x = 1.67 Inverse Tan x = Tan-1 1.67 = 59.1º 1st solution: x = 59.1º 2nd solution: x = 180 + 59.1 = 239.1° 4) Solve 2 + Sin x = 1.85 Negative Sin so quadrant 3 & 4 Subtract 2 Sin x = -0.15 x = Sin-1 0.15 = 8.6º Positive value 1st solution: x = 180 + 8.6 = 188.6º 2nd solution: x = 360 – 8.6 = 351.4°

  8. A S 0, 360 180 T C Home End 2 step solutions C 5) Solve 0.5Cos x + 3 = 2.6 Negative Cos so quadrant 2 & 3 Subtract 3 0.5Cos x = -0.4 Divide by 0.5 Cos x = -0.8 x = Cos-1 0.8 = 36.9º Positive value 1st solution: x = 180 – 36.9 = 143.1 ° 2nd solution: x = 180 + 36.9 = 216.9° The original graph y = 0.5Cosx + 3 y = 2.6 x = 143.9º & 216.9º

  9. A A A A A S S S S S 0, 360 0, 360 0, 360 0, 360 0, 360 180 180 180 180 180 T T T T T C C C C C Home End 3 step problems 1) Solve 2Sin(x + 25) = 1.5 2) Solve 5Cos(x + 33) = 4.8 3) Solve 2Tan(x – 25) = 8.34 4) Solve 5 + Sin(x + 45) = 4.85 5) Solve 0.5Cos(x + 32) + 4 = 3.85

  10. A A S S 0, 360 0, 360 180 180 T T C C Home End 3 Step solutions A 1) Solve 2Sin(x + 25) = 1.5 Sin(x + 25) = 0.75 x + 25 = Sin-1 0.75 = 48.6° so x = 23.6° x + 25 = 180 – 48.6 = 131.4° so x = 106.4° 2) Solve 5Cos(x + 33) = 4.8 Let A = x + 33 so 5Cos(A) = 4.8 Cos(A) = 0.96 And x = A – 33 A = Cos-1 0.96 = 16.3° or A = 360 – 16.3 = 343.7 So x = 16.3 – 33 = -16.7° or x = 343.7 – 33 = 310.7° But we need 2 solutions between 0 and 360! Next highest solution for A is A = 360 + 16.3 = 376.3° So x = 376.3° – 33 = 343.3° (or -16.7° + 360) Solutions: x = 310.7° and 343.3°

  11. A A S S 0, 360 0, 360 180 180 T T C C Home End 3 step solutions B 3) Solve 2Tan(x – 25) = 8.34 Tan(x – 25) = 4.17 x – 25 = Tan-1 4.17 = 76.5° so x = 101.5° x – 25 = 180 + 59.1 =256.5° so x = 281.5° 4) Solve 5 + Sin(x + 45) = 4.25 Sin(x + 45) = - 0.75 (Positive value) Sin-1 0.75 = 48.6° x + 45 = 180 + 48.6 = 228.6° so x = 183.6° x + 45 = 360 – 48.6 = 311.4° so x = 266.4°

  12. A S 0, 360 180 T C Home End 3 step solutions C 5) Solve 0.5Cos(x + 32) + 4 = 3.85 0.5Cos(x + 32) = -0.15 Cos(x + 32) = -0.3 Cos-10.3 = 72.5° x + 32 = 107.5° so x = 75.5 OR x + 32 = 252.5° so x = 220.5°

  13. Home End Multiple Solution Problems 1) Solve Sin(2X) = 0.6 2) Solve Cos(2X) = 0.8 3) Solve 5Tan(2X) = 8.4 4) Solve Sin(2X + 15) = 0.85 5) Solve 0.5Cos(0.5X) + 4 = 3.92

  14. A S 0, 360 180 T C Home End Multiple solutions A 1) Solve Sin(2x) = 0.6 Let A = 2x Sin(A) = 0.6 A = Sin-1 0.6 = 36.9° and A = 180 – 36.9 = 143.1° The next two solutions for A = 396.9° and A = 503.1° So A = 36.9°, 143.1°, 396.9°, 503.1° x = A ÷ 2 so x = 18.5° and 71.7° and 198.5° and 251.6° 2) Solve Cos(2x) = 0.8

  15. A A A S S S 0, 360 0, 360 0, 360 180 180 180 T T T C C C Home End Multiple solutions B 3) Solve 5Tan(2x) = 8.4 4) Solve Sin(2x + 15) = 0.85 5) Solve 0.5Cos(0.5x) + 4 = 3.92

  16. Home Overview: Trig Equations 1) Rearrange the equation into the form Sin A = eg) Solve 5Sin(2πx) = 4 Sin(2πx) = 0.8 2) Find a solution to the trig equation Check if degrees or radians! Where A = 2πx Sin(A) = 0.8 A = Sin-1 0.8 = 0.927 radians 3) Find several solutions for ‘A’ Using graph or unit circle Note πso use radians A = π – 0.927 = 2.214 rad 4) Use ‘A’ to find solutions for ‘x’ A = 0.927 or 2.214 Use each ‘A’ to find ‘x’ x = 0.927÷2π= 0.148 Where A = 2πx so x = A ÷ 2π x = 2.214÷ 2π= 0.352

More Related