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PreCalc/Trig-Chapter 4 E-mail: Skills/Concepts-In this chapter, you will find the values of coordinates of key points on the unit circle and see how they can be used to find the values of sine and cosine for any angle. You will generate parent graphs for sine and cosine and use them to sketch various transformations. You will define other trigonometric functions in terms of sine and cosine. You will also model situations using periodic functions. Guiding Questions- What does the unit circle tell you? How do you create a “wave” function? How do you shift trigonometric functions? Vocabulary/Key Ideas Angles and Coordinates in the Unit Circle Sine and Cosine in the Unit Circle The Fundamental Pythagorean Identity Using Right Triangles to Find Trigonometric Ratios Graphs and Transformations of Sine and Cosine The Five-Point Method for Graphing Sine and Cosine The Reciprocal Trig Functions Date Book Learning Target Section 4.1.1 4.1.2 Recall the special angles in a unit circle. Find the coordinates of the special angles in a unit circle. Learn how sine and cosine can be viewed in terms of the unit circle. Develop the Fundamental Pythagorean Identity. Use the unit circle, the Fundamental Pythagorean Identity, and right triangles, to find the values of trigonometric functions. Generate the graphs of sine and cosine using the unit circle. Find the domain, range, and intercepts for the sine and cosine graphs. Use shifts and vertical stretches to graph and find the equations of sinusoidal functions. Use the 5-point method to sketch graphs. 4.1.3 Other Trigonometric Functions in the Unit Circle Simplifying Complex Fractions Angular Frequency and Period The General Sine Function The Three Pythagorean Identities Verifying Identities Modeling with Periodic Functions Graphical Addition 4.1.4 Home Practice 4-7 to 4-14 4-24 to 4-31 4-38 to 4-46 4-53 to 4-57 4-59 to 4-61 Quiz 4.2.1 Be introduced to the reciprocal trig functions: cot, sec, and csc. Find values for these functions using the unit circle and a calculator. 4-70 to 4-78 4.2.2 4.2.3 4.2.4 4.3.1 4.3.2 Simplify trig expressions by rewriting the functions in terms of sine and cosine. Find special angles for trig ratios from the unit circle. Practice stretching a sine or cosine graph horizontally. Learn about angular frequency and its relationship to period. Derive the other two Pythagorean identities (sin²θ + cos²θ = 1 has already been done). Verify trig identities. Model a situation using sinusoidal curves. Graph a sum by adding corresponding coordinates. Observe that y = sin x + cos x is sinusoidal. Find the period and estimate the amplitude of y = sin x + cos x. 4-84 to 4-91 4-98 to 4-101 4-103 to 4-106 4-111 to 4-116, and 4-118 4-123 to 4-130 4-137 to 4-142 Team Test Chapter 4 Review Assignment Test Free Math Tutoring Tuesday 3:00 to 4:30 Ms. Guevara Room 2331 Wednesday 3:00 to 4:30 Ms. Guevara Room 2331 Thursday 3:00 to 4:30 Mr. Nicoletti Room 2334 Closure Problems