Determine the amplitude, range, period and phase shift of each, then sketch the graph: Include at least one full period.
1. y = 3sin( x + Π/4) +1
2. y = -cos(Π - 2x)+ 3
Determine the equations of the vertical asymptotes and all relative maximum and relative minimum points for two full periods, then sketch the graph:
3. y = -2csc(2x -Π )- 3
4. y = sec( 2x - Π/4) - 2
Determine the interval of a principal cycle and then identify the vertical asymptotes, the coordinates of the center point, and the coordinates of the halfway points. Sketch the graph.
5. y =1/2 tan ( 1/2.x + Π )
6. y = 5 + 3cot ( 3x + Π/3 )
Evaluate each to the nearest hundredth:
7. sin-1 (0.73)
8. cot-1 (-13)
Answer each:
9. Rewrite cot (sin-1 2x) as an algebraic expression involving the variable x. Assume that x > 0 and the angle is in quadrant I.
10. Using the graph of y = sin x , find all the exact values of x on the interval [- 7Π/2 , 5Π/3 ] that satisfy the ordered pair (x, √3/2).
11. Write the cosine function to fit the given graph:
