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Trig Graphs & Equations

Clyde Valley High School. Mathematics. S. Department. Presents. Trig Graphs & Equations. Menu. Graphs of Sine, Cosine and Tangent. The combined graphs. Summary. Solving trigonometric equations. Graphs. Graphs. Graphs. Graphs. What about tan 70 °?. tan 80 °?.

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Trig Graphs & Equations

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  1. Clyde Valley High School Mathematics S Department Presents Trig Graphs & Equations

  2. Menu Graphs of Sine, Cosine and Tangent The combined graphs Summary Solving trigonometric equations

  3. Graphs

  4. Graphs

  5. Graphs

  6. Graphs What about tan 70°? tan 80°? tan 85°? Can you explain what’s happening?

  7. 1 0 xº 90 180 270 360 -1 Graph of Sin x° Sin xº

  8. 1 0 xº 90 180 270 360 -1 Graph of Cos x° Cos xº

  9. 1 0 xº 90 180 270 360 This isn’t drawn to scale- but it looks something like this! -1 Graph of Tan x° Tan xº

  10. 1 0 xº 90 180 270 360 -1 Sin x ° +ve Cos x ° +ve Tan x ° +ve Combined Graphs Tan xº Cos xº 0 - 90° Sin xº

  11. 1 0 xº 90 180 270 360 -1 Sin x ° +ve Cos x ° -ve Tan x ° -ve Combined Graphs Tan xº Cos xº 90°-180° Sin xº

  12. 1 0 xº 90 180 270 360 -1 Sin x ° -ve Cos x ° -ve Tan x ° +ve Combined Graphs Tan xº Cos xº 180°-270° Sin xº

  13. 1 0 xº 90 180 270 360 -1 Sin x ° -ve Cos x ° +ve Tan x ° -ve Combined Graphs Tan xº Cos xº 270°-360° Sin xº

  14. Summary 90° 180° 0° 270°

  15. Sin x ° +ve Sin x ° +ve All Cos Tan Sin Cos x ° -ve Cos x ° +ve Tan x ° -ve Tan x ° +ve Sin x ° -ve Sin x ° -ve Cos x ° -ve Cos x ° +ve Tan x ° +ve Tan x ° -ve Summary 90° 180° 0° 270° Which are positive?

  16. All Summary 90° Sin x ° +ve Sin x ° +ve Sinners Cos x ° -ve Cos x ° +ve Tan x ° -ve Tan x ° +ve 180° 0° Sin x ° -ve Sin x ° -ve Take Care! Cos x ° -ve Cos x ° +ve Tan x ° +ve Tan x ° -ve 270° Which are positive?

  17. 1 0 xº 90 180 270 360 -1 Example 1 Cos x° = 0.5 0 ≤x⁰≤360 So x = 60° , 300° Cos xº 0.5 60° 300°

  18. Cos +ve Cos +ve 90° 60° 180° 0° 60° 270° Example 2 Cos x° = 0.5 0≤x⁰≤360 (Cos⁻¹ 0.5 = 60°) x = 60° , 300° S A 300° T C

  19. Sin -ve Sin -ve 90° 180° 0° 30° 30° 270° Example 3 Sin x° = -0.5 0≤x⁰≤360 (Sin⁻¹ 0.5 = 30°) x = 210° , 330° S A T C

  20. Sin +ve Sin +ve 90° 30º 30º 180° 0° 270° Example 4 2Sin x° = 1 0≤x⁰≤360 Sin x° = ½ (Sin⁻¹½ = 30°) x = 30° ,150° S A T C

  21. cos -ve cos -ve 90° 70.5° 180° 0° 70.5° 270° Example 5 0≤x⁰≤360 3 cos x°+1 = 0 3 cos x° = -1 cos x° = -⅓ (cos⁻¹ ⅓ = 70.5°) x = 109.5° , 250.5° S A T C

  22. Clyde Valley High School Mathematics S Department

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