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Review 6.1-6.4

Review 6.1-6.4. Find each value by referring to the graphs of the trig functions. 0. 0. -1. 0. Undefined. -1. sin (-720°) tan (-180°) cos (540°) tan ( π ) csc (4π) sec ( π ). Find the values of θ for which each equation is true. 270° + 360k° where k is any integer.

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Review 6.1-6.4

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  1. Review 6.1-6.4

  2. Find each value by referring to the graphs of the trig functions 0 0 -1 0 Undefined -1 sin (-720°) tan (-180°) cos (540°) tan (π) csc (4π) sec (π)

  3. Find the values of θ for which each equation is true. 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 sin θ = -1 sec θ = -1 tan θ = 0 sin θ = 0

  4. Graph each function on the given interval. 1.) y = sin x [-90° ≤ x ≤ 90°], scale of 45°

  5. Graph each function on the given interval. 1.) y = tan x [-π/2 ≤ x ≤ 3π/2], scale = π/4

  6. Graph each function on the given interval. 1.) y = cosx [-360° ≤ x ≤ 360°]

  7. Graph each function on the given interval. 1.) y = sec x [-360° ≤ x ≤ 360°]

  8. State the amplitude, period, and phase shift for each function. 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 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- )

  9. Write an equation of the sine function with each amplitude, period, and phase shift y = ± 0.75 sin(θ- 30°) y = ± 4 sin(120θ+3600°) 1.) Amp = 0.75, period = 360°, PS = 30° 2.) Amp = 4, period = 3°, PS = -30°

  10. Write an equation of the sine function with each amplitude, period, and phase shift y = ± 3.75 cos (4θ- 16°) y = ± 12 cos (8θ- 1440) 1.) Amp = 0.75, period = 360°, PS = 30° 2.) Amp = 4, period = 3°, PS = -30°

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

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

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

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

  15. 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.

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

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

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

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

  20. Find the values of x in the interval 0 ≤x ≤ 2π that satisfies the equation: 1. 2. 3. 4.

  21. Evaluate each expression. Assume all angles are in Quadrant I 1. 2.

  22. 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 = -cscx 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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