Practice - Graphs of Functions

**Practice** **In Exercises 1 and 2, identify the amplitude and period of the graph of the function.** 1. a. Amplitude: 1 Period: 2π b. Amplitude: 2 Period: 4π 2. a. Amplitude: 3 Period: 12 b. Amplitude: 5 Period: π **In Exercises 3-6, identify the amplitude and period of the function.** 3. g(x) = 3sin(x) Amplitude: 3 Period: 2π 4. g(x) = 4cos(x) Amplitude: 4 Period: 2π 5. g(x) = sin(2x) Amplitude: 1 Period: π 6. g(x) = 3cos(πx) Amplitude: 3 Period: 2 7. Which functions have an amplitude of 2 and a period of π? A. y = 2sin(2x) B. y = -2cos(πx) C. y = 4sin(2x) D. y = -2cos(2x) **In Exercises 9-12, graph the function.** 9. g(x) = sin(x) - 3 Amplitude: 1 Period: 2π Down 3 10. g(x) = cos(x + π/2) Amplitude: 1 Period: 2π Left π/2 11. g(x) = 2sin(x) + 1 Amplitude: 2 Period: 2π Up 1 12. g(x) = cos(2x + π) Amplitude: 1 Period: π Left π/2 **In Exercises 13 and 14, write a rule for g that represents the indicated transformations of the graph of f.** 13. f(x) = 2cos(x); translation 2 units down and 4 units left g(x) = 2cos(x + 4) - 2 14. f(x) = sin(4x); translation 1 unit up and 2 units right g(x) = sin(4(x - 2)) + 1 or g(x) = sin(4x - 8) + 1 **9.7 Practice** In Exercises 1-6, find the values of the other five trigonometric functions of θ. 1. sin θ = 2/3, 0 < θ < π/2 x^2 + 2^2 = 3^2 x^2 = 5 x = √5 sin θ = 2/3 cos θ = √5/3 tan θ = 2/√5 csc θ = 3/2 sec θ = 3/√5 cot θ = √5/2 2. cos θ = -3/5, π/2 < θ < π 5^2 = 3^2 + y^2 25 = 9 + y^2 16 = y^2 y = 4 sin θ = 4/5 cos θ = -3/5 tan θ = -4/3 csc θ = 5/4 sec θ = -5/3 cot θ = -3/4 3. tan θ = 4/7, π < θ < 3π/2 h^2 = 7^2 + 4^2 h^2 = 65 h = √65 sin θ = -4/√65 cos θ = -7/√65 tan θ = 4/7 csc θ = -√65/4 sec θ = -√65/7 cot θ = 7/4 4. cot θ = 5/4, π/2 < θ < π h^2 = 5^2 + 4^2 h^2 = 41 h = √41 sin θ = 4/√41 cos θ = -5/√41 tan θ = -4/5 csc θ = √41/4 sec θ = -√41/5 cot θ = 5/4 5. sec θ = 7/3, 3π/2 < θ < 2π 7^2 = 3^2 + y^2 49 = 9 + y^2 40 = y^2 y = √40 = 2√10 sin θ = -2√10/7 cos θ = 3/7 tan θ = -2√10/3 csc θ = -7/2√10 sec θ = 7/3 cot θ = -3/2√10 6. csc θ = 6/5, π < θ < 3π/2 6^2 = x^2 + 5^2 36 = x^2 + 25 11 = x^2 x = √11 sin θ = 5/6 cos θ = -√11/6 tan θ = -5/√11 csc θ = 6/5 sec θ = -6/√11 cot θ = -√11/5