Worksheet 15 KEY - Graphing Trigonometric Functions PDF

M110 Fa17 Page 1/7 Worksheet 15 KEY - Graphing Trigonometric Functions y 1. y = 3 sin(x)...

M110 Fa17 Page 1/7 Worksheet 15 KEY - Graphing Trigonometric Functions y 1. y = 3 sin(x) 3 Period: 2π Amplitude: 3 Phase Shift: 0 Vertical Shift: 0 π π 3π 2π x 2 2 −3 y 2. y = sin(3x) 2π 1 Period: 3 Amplitude: 1 Phase Shift: 0 Vertical Shift: 0 π π π 2π x 6 3 2 3 −1 y 3. y = −2 cos(x) Period: 2π 2 Amplitude: 2 Phase Shift: 0 Vertical Shift: 0 π 2 π 3π 2π x 2 −2  π y 4. y = cos x − 2 Period: 2π 1 Amplitude: 1 π Phase Shift: 2 Vertical Shift: 0 π π 3π 2π 5π x 2 2 2 −1 M110 Fa17 Page 2/7  π y 5. y = − sin x + 3 Period: 2π 1 Amplitude: 1 π Phase Shift: − 3 Vertical Shift: 0 − π3 π 6 2π 7π 5π x 3 6 3 −1 y 6. y = sin(2x − π) Period: π 1 Amplitude: 1 π Phase Shift: 2 Vertical Shift: 0 π 3π π 5π 3π 2 4 4 2 x −1 1  1 π  y 7. y = − cos x+ 1 3 2 3 3 Period: 4π 1 Amplitude: 3 x − 2π 4π 7π 10π π 2π 3 Phase Shift: − 3 3 3 3 3 Vertical Shift: 0 − 13 y 8. y = cos(3x − 2π) + 4 2π 5 Period: 3 Amplitude: 1 4 2π Phase Shift: 3 3 Vertical Shift: 4 2π 5π π 7π 4π x 3 6 6 3 M110 Fa17 Page 3/7  π y 9. y = sin −x − −2 4 Period: 2π − 9π 7π 5π 3π − π π 3π 5π 7π x 4 − 4 − 4 − 4 4 4 4 4 4 Amplitude: 1 π −1 Phase Shift: − (You need to use  4π  y = − sin x + − 2 to find this.)1 −2 4 Vertical Shift: −2 −3 2 π  10. y = cos − 4x + 1 3 2 y π Period: 5 2 3 2 Amplitude: 3 1 π Phase Shift: (You need to use 8 2  π 1 y = cos 4x − + 1 to find this.)2 3 3 2 Vertical Shift: 1 − 3π − π4 − π8 3π 5π π π π 8 8 4 8 2 8 x 3  π 1 y 11. y = − cos 2x + − 2 3 2 1 Period: π 3 Amplitude: 2 x π − π6 π π 7π 5π Phase Shift: − − 12 12 3 12 6 6 1 Vertical Shift: − 2 −2 y 12. y = 4 sin(−2πx + π) 4 Period: 1 Amplitude: 4 1 Phase Shift: (You need to use 2 3 x y = −4 sin(2πx − π) to find this.) − 12 − 41 1 1 3 1 5 3 4 2 4 4 2 Vertical Shift: 0 −4 1 Two cycles of the graph are shown to illustrate the phase shift. 2 Again, we graph two cycles to illustrate the phase shift. 3 This will be the last time we graph two cycles to illustrate the phase shift. M110 Fa17 Page 4/7  π y 13. y = tan x − 3 Period: π 1 − π6 π 12 π 3 7π 5π x −1 12 6  1  y 14. y = 2 tan x −3 4 Period: 4π −2π −π π 2π x −1 −3 −5 1 y 15. y = tan(−2x − π) + 1 3 is equivalent to 1 4 y = − tan(2x + π) + 1 3 3 1 via the Even / Odd identity for tangent. 2 π 3 Period: 2 − 3π 5π − π 4 − 8 3π 2 − 8 − π4 x M110 Fa17 Page 5/7
y 16. y = sec x − π2
Start with y = cos x − π2 Period: 2π 1 π π 3π 2π 5π x 2 2 2 −1  π y 17. y = − csc x + 3  π Start with y = − sin x + 3 Period: 2π 1 − π3 π 2π 7π 5π x 6 3 6 3 −1 1  1 π  y 18. y = − sec x+ 3 2 3   1 1 π Start with y = − cos x+ 3 2 3 Period: 4π 1 3 10π x − 2π 4π 7π π 3 3 3 3 3 − 13 M110 Fa17 Page 6/7 y 19. y = csc(2x − π) Start with y = sin(2x − π) Period: π 1 π 3π π 5π 3π x 2 4 4 2 −1 y 20. y = sec(3x − 2π) + 4 Start with y = cos(3x − 2π) + 4 2π Period: 3 5 4 3 2π 5π π 7π 4π x 3 6 6 3  π y 21. y = csc −x − −2 4  π Start with y = sin −x − −2 4 Period: 2π x − π4 π 3π 5π 7π 4 4 4 4 −1 −2 −3 M110 Fa17 Page 7/7  π y 22. y = cot x + 6 Period: π 1 − π6 π π 7π 5π x 12 3 12 6 −1  1  y 23. y = −11 cot x 5 Period: 5π 11 5π 5π 15π 5π x 4 2 4 −11 1  3π  y 24. y = cot 2x + +1 3 2 π Period: 2 4 3 1 2 3 − 3π 5π − π 4 − 8 3π − π 2 − 8 4 x