1 / 41

Mastering Inverse Trigonometric Functions: Examples & Tests

This lesson focuses on inverse trigonometric functions, how to evaluate them, find trigonometric values, and apply them in real-world scenarios. Practice checks are provided with detailed examples and standardized test questions. Learn about phase shift, amplitude, period, and translating sine functions. Discover how to solve equations using inverse trigonometric functions and identify arc functions. Explore angles, values, and keystrokes needed for calculations using unit circles and calculators. Enhance your trigonometry skills with multiple practice scenarios and step-by-step solutions.

brendahester
Download Presentation

Mastering Inverse Trigonometric Functions: Examples & Tests

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. Splash Screen

  2. Five-Minute Check (over Lesson 12–8) CCSS Then/Now New Vocabulary Key Concept: Inverse Trigonometric Functions Example 1: Evaluate Inverse Trigonometric Functions Example 2: Find a Trigonometric Value Example 3: Standardized Test Example Example 4: Real-World Example: Use Inverse Trigonometric Functions Lesson Menu

  3. State the phase shift for y = 2 cos (x + 60°). A. –60° B. –30° C. 60° D. 120° 5-Minute Check 1

  4. State the phase shift for y = 2 cos (x + 60°). A. –60° B. –30° C. 60° D. 120° 5-Minute Check 1

  5. State the vertical shift for y = 2 sin 3x + . A.– B.2 C. D. 1 1 1 1 __ __ __ __ 2 2 2 4 5-Minute Check 2

  6. State the vertical shift for y = 2 sin 3x + . A.– B.2 C. D. 1 1 1 1 __ __ __ __ 2 2 2 4 5-Minute Check 2

  7. State the amplitude of y = –1 + 3 sin A. 1 B. 2 C. 3 D. 4 5-Minute Check 3

  8. State the amplitude of y = –1 + 3 sin A. 1 B. 2 C. 3 D. 4 5-Minute Check 3

  9. State the period of y = cos A. 180º B. 1080º C. 2160º D. 3240º 5-Minute Check 4

  10. State the period of y = cos A. 180º B. 1080º C. 2160º D. 3240º 5-Minute Check 4

  11. Identify the equation of a sine function that has a graph that is the graph of the parent function translated 5 units up and 3 units left. A.y = 5 sin (x + 3) B.y = sin (x – 3) + 5 C.y = sin (x + 3) + 5 D.y = 3 sin (x + 5) 5-Minute Check 5

  12. Identify the equation of a sine function that has a graph that is the graph of the parent function translated 5 units up and 3 units left. A.y = 5 sin (x + 3) B.y = sin (x – 3) + 5 C.y = sin (x + 3) + 5 D.y = 3 sin (x + 5) 5-Minute Check 5

  13. Content Standards A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Mathematical Practices 7 Look for and make use of structure. CCSS

  14. You graphed trigonometric functions. • Find values of inverse trigonometric functions. • Solve equations by using inverse trigonometric functions. Then/Now

  15. principal values • Arcsine function • Arccosine function • Arctangent function Vocabulary

  16. Concept

  17. A.Find the value of . Write the angle measure in degrees and radians. Find the angle  for –90° ≤  ≤ 90° that has a sine value of . Evaluate Inverse Trigonometric Functions Example 1

  18. Find a point on the unit circle that has an x-coordinate of . When  = 45°, sin  = . So, = 45° or . Evaluate Inverse Trigonometric Functions Method 1 Use a unit circle. Example 1

  19. Keystrokes: ) ) 2nd 2nd ÷ [SIN–1] [ ] 2 2 45 ENTER Evaluate Inverse Trigonometric Functions Method 2 Use a calculator. Answer: Example 1

  20. Keystrokes: ) ) 2nd 2nd ÷ [SIN–1] [ ] 2 2 45 ENTER Answer: Therefore, = 45° or . Evaluate Inverse Trigonometric Functions Method 2 Use a calculator. Example 1

  21. ) 2nd (–) ENTER Keystrokes: [SIN–1] 1 –90 Evaluate Inverse Trigonometric Functions B.Find the value of Arcsin (–1). Write the angle measure in degrees and radians. Find the angle  for –90° ≤  ≤ 90° that has a sine value of –1. Answer: Example 1

  22. ) 2nd (–) ENTER Keystrokes: [SIN–1] 1 –90 Answer: Therefore, Arcsin (–1) = –90° or – . Evaluate Inverse Trigonometric Functions B.Find the value of Arcsin (–1). Write the angle measure in degrees and radians. Find the angle  for –90° ≤  ≤ 90° that has a sine value of –1. Example 1

  23. A. Find the value of Cos–1 . Write the angle measure in degrees and radians. A.60° or B.90° or C.180° or  D.45° or Example 1

  24. A. Find the value of Cos–1 . Write the angle measure in degrees and radians. A.60° or B.90° or C.180° or  D.45° or Example 1

  25. A.60° or B.90° or C.180° or  D.45° or B. Find the value of Arccos(–1). Write the angle measure in degrees and radians. Example 1

  26. A.60° or B.90° or C.180° or  D.45° or B. Find the value of Arccos(–1). Write the angle measure in degrees and radians. Example 1

  27. Find the value of Round to the nearest hundredth. Keystrokes: 7 4 ) TAN 2nd ) [COS–1] ÷ ENTER 1.436140662 Find a Trigonometric Value Answer: Example 2

  28. Find the value of Round to the nearest hundredth. Keystrokes: 7 4 ) TAN 2nd ) [COS–1] ÷ ENTER 1.436140662 Find a Trigonometric Value Answer: 1.44 Example 2

  29. Find the value of Write the angle measure in radians. Round to the nearest hundredth. A. 1.5 radians B. 1.12 radians C. 1.04 radians D. 1.62 radians Example 2

  30. Find the value of Write the angle measure in radians. Round to the nearest hundredth. A. 1.5 radians B. 1.12 radians C. 1.04 radians D. 1.62 radians Example 2

  31. If cos  = –0.86, find . A –149.3° B –59.3° C 59.3° D 149.3° Read the Test Item The cosine of angle  is 0.86. This can be written as Arccos (0.86) = . Example 3

  32. Keystrokes: 2nd ENTER 149.3165829 ) [COS–1] (–) 0.86 Solve the Test Item Use a calculator. Answer: Example 3

  33. Keystrokes: 2nd ENTER 149.3165829 ) [COS–1] (–) 0.86 Solve the Test Item Use a calculator. Answer: So,  = 149.3. The answer is D. Example 3

  34. If sin  = –0.707, find . A. –30° B. –45° C. 60° D. 75° Example 3

  35. If sin  = –0.707, find . A. –30° B. –45° C. 60° D. 75° Example 3

  36. Use Inverse Trigonometric Functions WATER SKIING A water ski ramp is 5.5 feet tall and 12 feet long, as shown below. Write an inverse trigonometric function that can be used to find . Then find the measure of . Round to the nearest tenth. Example 4

  37. Use Inverse Trigonometric Functions Because the measures of the opposite side and the hypotenuse are known, you can use the sine function. Sine function Inverse sine function  ≈ 27.3° Use a calculator. Answer: Example 4

  38. Use Inverse Trigonometric Functions Because the measures of the opposite side and the hypotenuse are known, you can use the sine function. Sine function Inverse sine function  ≈ 27.3° Use a calculator. Answer: So, the angle of the ramp is about 27.3°. Example 4

  39. A. B. C. D. WATER SKIING A water ski ramp is 8 feet tall and 20 feet long. Write an inverse trigonometric function that can be used to find . Then find the measure of . Round to the nearest tenth. Example 4

  40. A. B. C. D. WATER SKIING A water ski ramp is 8 feet tall and 20 feet long. Write an inverse trigonometric function that can be used to find . Then find the measure of . Round to the nearest tenth. Example 4

  41. End of the Lesson

More Related