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Chapter 8 Final Exam Review

Chapter 8 Final Exam Review. THE BEST CLASS EVER…ERRR…. PRE-CALCULUS. Chapter 8 Previous Lesson Materials. What was C hapter 8 about?. Graphing Trig Functions Amplitude Period Vertical Shift Phase Shift. x. 0. sin x. 0. 1. 0. -1. 0. y = sin x. y. x.

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Chapter 8 Final Exam Review

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  1. Chapter 8 Final Exam Review THE BEST CLASS EVER…ERRR…. PRE-CALCULUS

  2. Chapter 8Previous Lesson Materials

  3. What was Chapter 8 about? • Graphing Trig Functions • Amplitude • Period • Vertical Shift • Phase Shift

  4. x 0 sin x 0 1 0 -1 0 y = sin x y x Graph of the Sine Function To sketch the graph of y = sin x first locate the key points.These are the maximum points, the minimum points, and the intercepts. Then, connect the points on the graph with a smooth curve that extends in both directions beyond the five points. A single cycle is called a period.

  5. Transformations of Trig Functions • Amplitude |A|: A controls vertical stretching/shrinking • Period p can be in radians or degrees: p is the horizontal length to complete one cycle • B can be in radians or degrees:B controls horizontal stretching/shrinking

  6. Vertical Stretching/Shrinking of Sine Functions KEY TAKE-AWAY: x-intercepts are unchanged; multiply y-value of max/min by A.

  7. Axis of the Wave Phase Shift • Shift each point left or right based on the value of h. Remember it is (x-h)! The horizontal line midway between the maximum and minimum points of the curve. The shift of the x-axis. Amplitude should be found from this axis.

  8. Writing an Equation Steps: Remember your forms Identify the amplitude Determine the period and solve for b Identify your axis of the wave to find vertical shift Choose a point close to x=0 to determine the horizontal shift.

  9. What was Chapter 8 about? • Graphing Trig Functions • Amplitude • Period • Vertical Shift • Phase Shift • Basic Trig Identities • Simplifying • Solving

  10. RECIPROCAL IDENTITIES QUOTIENT IDENTITIES PYTHAGOREAN IDENTITIES Note It may be necessary to recognize alternative forms of the identities above, such as sin²  =1 – cos²  and cos²  =1 – sin² .

  11. Suggestions Start with the more complicated side Try substituting basic identities (changing all functions to be in terms of sine and cosine may make things easier) Try algebra: factor, multiply, add, simplify, split up fractions If you’re really stuck make sure to: Change everything on both sides to sine and cosine. Work with only one side at a time!

  12. How to get proficient at verifying identities: Once you have proved an identity go back to it, redo the verification or proof without looking at how you did it before, this will make you more comfortable with the steps you should take. Redo the examples done in class using the same approach, this will help you build confidence in your instincts!

  13. Steps for Solving: • Isolate the Trigonometric function. • Then solve for the angle exactly if the ratio represents known special triangle ratios. • Or solve for the angle approximately using the appropriate inverse trigonometric function. • DO NOT DIVIDE BY A TRIG FUNCTION!!!!

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