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Name: __________________________________________________________________ Horizontal and Vertical Shift of Sine and Cosine Curve y = a sin b(x + c) + d y = a cos b(x + c) + d a = amplitude b = frequency c = horizontal shift (opposite direction) +c moves graph _________________ -­‐c moves graph _________________ Date: ________________ Period: ______________ d = vertical shift (same direction) +d moves graph _______________ -­‐d moves graph ________________ 1. Which of the following relations has the 2. Which of the following is an equation of a same graph as y = 3 sin x? sine curve with a maximum value of 3, 2
minimum value of 1 and period of ? 3
A) y = -­‐3 sin x C) y = 3 cos x π
π
B) y = 3 cos (x + ) D) y = -­‐3 cos(x + ) A) y = sin 6x + 1 C) y = 2 sin 3x 2
2
B) y = sin 3πx + 2 D) y = sin 6πx + 1 3. What is the amplitude of the graph of 4. What is the amplitude of the graph shown in the accompanying graph? A) 1.5 C) 6 B) 2 D) 12 5. What is the period of the function 1
2
A) C) π 2
3
1
B) D) 6π 3
7. What is the maximum value of the function y = 3sin2x? A) π C) 3 B) 2 D) 2π 9. The path traveled by a roller coaster is modeled by the equation y = 27sin13x + 30. What is the maximum altitude of the roller coaster? A) 13 C) 30 B) 27 D) 57 6. The brightness of the star MIRA over time is π
given by the equation y = 2sin x + 6, where x 4
represents time and y represents brightness. What is the period of this function, in radians? 8. What is the maximum value of y for the equation y = 3sinx + 1? A) 1 C) 3 B) 2 D) 4 10. Which equation best represents the pattern shown in the graph below? Mixed Review: 11. Find B to the nearest degree: 12. Find the value of the expression,
13. What is the amplitude of the graph of the 14. The graph of which function has
Name: __________________________________________________________________ Horizontal and Vertical Shift of Sine and Cosine Curve HOMEWORK Date: ________________ Period: ______________ 9) What equation is represented by the graph below? 10) What equation is represented by the graph below?
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