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Pick up handout: Trig Function Decimal Approximations Fill in the radians column and reference angle column Use your calculator to find the decimal approximations for the six trig functions and fill in the rest of the table

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Find the exact value of each of the following:

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On Monday 8 minute time limit All or nothing Must be turned in by the end of 8 minutes to count.

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Section 4.5 Have out your graphs that you made.

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(x, y) = (cos θ, sin θ) If we want a graph of sin θ, we can plot y-values as a function of θ. ◦ You did this in the Making Waves activity If we want a graph of cos θ, we can plot x-values as a function of θ.

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Cyclical (repeats) Continuous Goes through origin Has an amplitude of 1 Has a period of 2π Domain=ℝ (all real #s) Range = [-1, 1] Odd function ◦ Rotational symmetry

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Amplitude = |A| = the half-height of the curve Period = 2π/B ◦ The length of one cycle ◦ The horizontal distance between consecutive corresponding points Phase Shift = C/B = distance the curve is shifted right Vertical Shift = D = distance the curve is shifted up

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http://www.intmath.com/trigonometric- graphs/3-graphs-sin-cos-phase- shift.php#java http://www.intmath.com/trigonometric- graphs/3-graphs-sin-cos-phase- shift.php#java http://www.analyzemath.com/trigonometry/ sine.htm http://www.analyzemath.com/trigonometry/ sine.htm

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Determine the amplitude, period, phase shift, and vertical shift of the function.

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Cyclical (repeats) Continuous y-intercept at (0, 1) Has an amplitude of 1 Has a period of 2π Domain=ℝ (all real numbers) Range = [-1, 1] Even function ◦ Symmetric across y-axis

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Amplitude = |A| = the half-height of the curve Period = 2π/B ◦ The length of one cycle ◦ The horizontal distance between consecutive corresponding points Phase Shift = C/B = distance the curve is shifted right Vertical Shift = D = distance the curve is shifted up

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http://www.intmath.com/trigonometric- graphs/3-graphs-sin-cos-phase- shift.php#java http://www.intmath.com/trigonometric- graphs/3-graphs-sin-cos-phase- shift.php#java http://www.analyzemath.com/cosine/cosine. html http://www.analyzemath.com/cosine/cosine. html

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Determine the amplitude, period, phase shift, and vertical shift of the function.

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Determine the amplitude, period, phase shift, and vertical shift of the function. Then graph.

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Page 493 #1-49 Every Other Odd Use graph paper for graphs Check graphs with your TI-83

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In Exercises 1-6, determine the amplitude of each function. Then graph the function and y=sin(x) in the same rectangular coordinate system for 0≤x≤2π. In Exercises 7-16, determine the amplitude and period of each function. Then graph one period of the function.

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1. Draw your x-axis and y-axis 2. Number your positive x-axis. Start at 0, and place each angle (in radians) that is on the unit circle on your x-axis. Keep consistent spacing! 3. Number your negative x-axis. Do the same thing, but in the opposite direction and include negative signs. 4. Number your y-axis. 5. Draw dashed lines for any asymptotes. 6. Draw points, such as (π/6, sin(π/6)) (π/6,.5) 7. Connect the points to make a smooth curve.

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2.6 Graphs of the Sine and Cosine Functions xxy = sin x 00=SIN(B2) π/6=PI()/6=SIN(B3) π/3=PI()/3=SIN(B4) π/2=PI()/2=SIN(B5) 2π/3=B5+PI()/6=SIN(B6) 5π/6=B6+PI()/6=SIN(B7)

2.6 Graphs of the Sine and Cosine Functions xxy = sin x 00=SIN(B2) π/6=PI()/6=SIN(B3) π/3=PI()/3=SIN(B4) π/2=PI()/2=SIN(B5) 2π/3=B5+PI()/6=SIN(B6) 5π/6=B6+PI()/6=SIN(B7)

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