6.0 Lesson_Trigonometric_Fns

6.0 Lesson_Trigonometric_Fns - d = horizontal translation...

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Lesson_6.0_Trigonometric_Functions.notebook 1 November 04, 2009 5.0 Trigonometry Review (Getting Ready) Unit 5: Trigonomatric Functions Recall All trigonometric ratios are defined in terms of the sides of a right triangle. When the rotation exceeds 90, we relate the angle to the coordinate axes and express the ratios in terms of x, y and r. NOTE: θ θ θ θ y x I II III IV r y x Opp Hyp Adj P (x, y) Unit Circle Pythagorean Theorem : x 2 + y 2 = r 2 ; r≥0 Definitions:
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Lesson_6.0_Trigonometric_Functions.notebook 2 November 04, 2009 Example 1: a) sin(180 o - θ ) b) cos(180 o + θ ) c) sin(360 o - θ ) d) tan(- θ ) e) csc(180 o + θ ) Simplify in terms of θ . C A S T Example 2: a) b) c) d) e) f) g) Special triangles
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Lesson_6.0_Trigonometric_Functions.notebook 3 November 04, 2009 Find all θ , θ ε [0, 360 ] to the nearest degree. o a) tan θ =1.4387 b) tan θ =-0.2358 Example 3: a = amplitude k = 360 period o c = vertical translation up/down or equation of axis
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Unformatted text preview: d = horizontal translation left/right or phase shift Sinusoidal Functions: y = sin x y = cos x Lesson_6.0_Trigonometric_Functions.notebook 4 November 04, 2009 a)State the equation of a cosine function with the following properties: b) Find its domain and range for 2 cycles starting at zero . Example 4: V stretch 3 H stretch 18 H right 5 V down 2 R in X axis • amplitude = 3 • period = 20 • phase shift 5 right • EOA y = -2 • graph starts at min y = -3 cos(18 θ-5)-2 D = { θ∈R} R = {y ∈R|-5≤y≤1} Example 5 Sketch y = -2cos( θ + 30 ) + 1 for one cycle. o 2 1 • amplitude = • period = • phase shift = • EOA y Lesson_6.0_Trigonometric_Functions.notebook 5 November 04, 2009 Homework page 314 #1-7...
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6.0 Lesson_Trigonometric_Fns - d = horizontal translation...

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