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Review

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**Find each value by referring to the graphs of the trig functions**

sin (-720°) tan (-180°) cos (540°) tan (π) csc (4π) sec (π) -1 Undefined -1

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**Find the values of θ for which each equation is true.**

sin θ = -1 sec θ = -1 tan θ = 0 sin θ = 0 270° + 360k° where k is any integer 180° + 360k° where k is any integer 180k° where k is any integer 180k° where k is any integer

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**Graph each function on the given interval.**

1.) y = sin x [-90° ≤ x ≤ 90°], scale of 45°

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**Graph each function on the given interval.**

1.) y = tan x [-π/2 ≤ x ≤ 3π/2], scale = π/4

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**Graph each function on the given interval.**

1.) y = cos x [-360° ≤ x ≤ 360°]

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**Graph each function on the given interval.**

1.) y = sec x [-360° ≤ x ≤ 360°]

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**State the amplitude, period, and phase shift for each function.**

1.) y = -2sin θ 2.) y = 10sec θ 3.) y = -3sin 4θ 4.) y = 0.5sin (θ- ) 5.) y = 2.5 cos(θ + 180°) 6.) y = -1.5sin (4θ- ) Amp = 2 Per = 360° PS = 0° Amp = 10 Per = 360° PS = 0° Amp = 3 Per = 90° PS = 0° Amp = 0.5 Per = 360° PS = right Amp = 2.5 Per = 360° PS = 180° left Amp = 1.5 Per = 90° PS = right

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**Write an equation of the sine function with each amplitude, period, and phase shift**

1.) Amp = 0.75, period = 360°, PS = 30° 2.) Amp = 4, period = 3°, PS = -30° y = ± 0.75 sin(θ- 30°) y = ± 4 sin(120θ+3600°)

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**Write an equation of the sine function with each amplitude, period, and phase shift**

1.) Amp = 0.75, period = 360°, PS = 30° 2.) Amp = 4, period = 3°, PS = -30° y = ± 3.75 cos (4θ- 16°) y = ± 12 cos (8θ- 1440)

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Graph each function: 1.) y = 0.5 sin x

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Graph each function: 1.) y = 2 cos (3x)

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Graph each function: 1.) y = 2 cos (2x – 45°)

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Graph each function: 1.) y = tan (x + 60°)

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**Find the exact value of each expression without using a calculator**

Find the exact value of each expression without using a calculator. When your answer is an angle, express it in radians. Work out the answers yourself before you click.

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Answers for problems 1 – 9. Negative ratios for arccos generate angles in Quadrant II. y x 1 2 The reference angle is so the answer is

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y x -1 2 14. x 1 2 y 15.

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Graph each function: 1.) y = -2cos (3θ), scale π/4, -2π ≤ θ ≤ 2π

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Graph each function: 1.) y = ½ cos(x – π/2)

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**Find the values of x in the interval 0 ≤x ≤ 2π that satisfies the equation:**

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**Evaluate each expression. Assume all angles are in Quadrant I**

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**Quick Quiz Find the values of θ for which the equation**

tan θ = 1 is true. State the domain and range for the function y = -csc x State the amplitude, period, and phase shift of: Write an equation of the cosine function with amplitude 7, period π, and phase shift 3π/2 45°+180°k D = all reals except 180°k R = y ≤ -1 or y ≥ 1 A = ⅓ PS = -π/6 P = 2π

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5.3 Solving Trigonometric Equations. What are two values of x between 0 and When Cos x = ½ x = arccos ½.

5.3 Solving Trigonometric Equations. What are two values of x between 0 and When Cos x = ½ x = arccos ½.

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