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Use Trigonometry with Right Triangles & Define General Angles

Use Trigonometry with Right Triangles & Define General Angles. Notes 20 – Sections 13.1 & 13.2. Essential Learnings. Students will understand and be able to identify trigonometric ratios. Students will be able to use trigonometric ratios to solve problems.

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Use Trigonometry with Right Triangles & Define General Angles

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  1. Use Trigonometry with Right Triangles & Define General Angles Notes 20 – Sections 13.1 & 13.2

  2. Essential Learnings • Students will understand and be able to identify trigonometric ratios. • Students will be able to use trigonometric ratios to solve problems. • Students will be able to define general angles.

  3. Trigonometry • Comes from the Greek words: Trigonos – triangle Metron - measurement • Bring calculators to every class!

  4. Trigonometry Consider a right triangle with an acute angle θ (theta). Hypotenuse Opposite side θ Adjacent side

  5. Trigonometric Ratios There are six trigonometric functions: Sine Cosecant Cosine Secant Tangent Cotangent

  6. Sine & Cosecant

  7. Cosine & Secant

  8. Tangent & Cotangent

  9. Example 1 Evaluate the trig functions. sin θ = _____ cscθ = _____ cosθ = _____ sec θ = _____ tan θ = _____ cot θ = _____ 17 8 θ 15

  10. Example 2 Evaluate the trig functions. sin θ = _____ cscθ = _____ cosθ = _____ sec θ = _____ tan θ = _____ cot θ = _____ 2 θ 4

  11. Class Problem Find the missing side then find the ratios for  θ. sin θ = _____ cscθ = _____ cosθ = _____ sec θ = _____ tan θ = _____ cot θ = _____ 25 θ 7

  12. Example 3: Finding Angles To find the angle, use inverse trig functions: sin-1θ cos-1θ tan-1θ Find angles A and B.

  13. Example 4: Solving Triangles Solving a triangle means finding all of the missing angles and sides.

  14. Example 5 You are measuring the height of a building that is 22 feet away. The angle of elevation from you to the top of the building is 58°. What is the height?

  15. Class Problem A kite makes an angle of 64° with the ground. If the string on the kite is 30 feet, how far above the ground is the kite? (Round to the nearest foot.)

  16. Special Triangles

  17. Special Angles

  18. Vocabulary Standard Position Angles – an angle in the coordinate plane rotated counter clockwise from the positive x-axis Initial Side– the side on the positive x-axis

  19. Vocabulary Terminal Side – the side of the angle that is rotated Coterminal Angles – two angles that share the same terminal side

  20. Angles in Standard Position

  21. Example 6 Draw an angle with the given measure in standard position. a) 45 b) 405

  22. Example 6 cont. Draw an angle with the given measure in standard position. c) - 45 d) - 570

  23. Example 7 Find a positive and negative coterminal angle with 230. Positive: Negative: There is an infinite number of coterminal angles.

  24. Class Problems • Draw a 420 angle in standard position. • Find a positive and negative coterminal angle with 135.

  25. Assignment Page 856: 3 – 15 (x3), 17 – 19, 21 Page 862: 3 – 9 (x3), 15, 18 WS 1 – Right Triangle Trigonometry

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