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Right Triangle Trigonometry

Right Triangle Trigonometry. 23 March 2011. Degree Mode v. Radian Mode. Symbols. Theda – Represents the angle measure. Adjacent Side. Hypotenuse. Opposite Side. Six Trigonometric Ratios. 3 Basic Ratios + 3 Reciprocal Ratios What is a reciprocal?. Basic Trig. Ratio Sine Cosine

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Right Triangle Trigonometry

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  1. Right Triangle Trigonometry 23 March 2011

  2. Degree Mode v. Radian Mode

  3. Symbols Theda – Represents the angle measure Adjacent Side Hypotenuse Opposite Side

  4. Six Trigonometric Ratios • 3 Basic Ratios + 3 Reciprocal Ratios • What is a reciprocal?

  5. Basic Trig. Ratio Sine Cosine Tangent Reciprocal Trig. Ratio Cosecant Secant Cotangent Six Trigonometric Ratios, cont. It’s a sin to have two c’s.

  6. Three Basic Trig. Ratios SOH-CAH-TOA

  7. Sine (SOH) 24 25 7

  8. Cosine (CAH) 24 25 7

  9. Tangent (TOA) 24 25 7

  10. Cosecant – Reciprocal of Sine (“It’s a sin to have two C’s.”) 24 25 7

  11. Secant – Reciprocal of Cosine 24 25 7

  12. Cotangent – Reciprocal of Tangent 24 25 7

  13. Your Turn: • Pg. 419: 9 – 14, 27 – 32

  14. Solving for Side Lengths • If given one side and one angle measure, then we can solve for any other side of the triangle. 8 x

  15. Solving Right Triangles, cont. • Ask yourself what types of sides do you have: opposite, adjacent, and/or hypotenuse? • Pick the appropriate trig function to solve for x. • Solve for x. 8 x

  16. Solving for Side Lengths, cont. 8 x

  17. Solving Side Lengths, cont. x 14

  18. Special Trigonometric RatiosMemorize These!!!

  19. Your Turn:

  20. Inverse Trigonometric Ratios • We can “undo” trig ratios • Gives us the angle measurement (theda) • Represented by a small –1 in the upper right hand corner • Ex. • 2nd button → correct trig ratio

  21. Inverse Trigonometric Ratios, cont.

  22. Your Turn: Solve for thedaRound to nearest hundredth

  23. Solving For Angle Measures • If given two sides of a triangle, then we can solve for any of the angles of the triangle. 4 5

  24. Solving for Angle Measures, cont. • Ask yourself what types of sides do you have: opposite, adjacent, and/or hypotenuse? • Pick the appropriate trig function to solve for • Solve for using the inverse trigonometric function 4 5

  25. Solving for Angle Measures, cont. 4 5

  26. Your Turn: • Complete problems 11 – 16 on the Solving Right Triangles Practice handout

  27. Solving Right Triangles • We can use two properties of triangles to solve for all the angles and the side lengths of a right triangle.

  28. Pythagorean Theorem For a righttriangle, a2 + b2 = c2 Triangle Sum Theorem When you add up all the angles in a triangle, they equal 180° Properties of Triangles

  29. Given Two Sides Use Pythagorean Theorem to solve for remaining side. Solve for 1 of the angles using trig ratios Solve for the other angle using Triangle Sum Theorem Given an Angle & a Side Use the Triangle Sum Theorem to solve for the other angle Use trig ratios to solve for 1 of the sides Use the Pythagorean Theorem to solve for the other side Tricks for Solving Right Triangles

  30. Beta – Another symbol for an unknown angle measure

  31. Solving Right Triangles – Examples: Given Two Sides 4 5

  32. Solving Right Triangles – Examples: Given an Angle and a Side 2 30°

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