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Introduction to Sine Graphs
Warm-up (2:30 m)• For the graph below, identify the max, min, y-
int, x-int(s), domain and range.
Fill in the table below. Then use the points to sketch the graph of y = sin t
t 0
sin t2
π4
π4
π3
π 2π2π3
4π5
4π7
4π
2π
4π3 π 2π4
π52
π34
π7
Reflection Questions
3. What is the max of y = sin t? What is the min?
4. What is the y-int? What are the x-intercepts?
5. What is the domain? What is the range?
Reflection Questions, cont.6. What do you think would happen if you
extended the graph beyond 2π?
7. How would extending the graph affect the domain and the x-intercepts?
Periodicity• Trigonometric graphs are
periodic because the pattern of the graph repeats itself
• How long it takes the graph to complete one full wave is called the period
0
2
–21 Period 1 Period
Period: π
π 2π
Periodicity, cont.
2t
sin)t(f )t4sin()t(f
2 2
–2 –2
–2π
2π –π
π
Your Turn:• Complete problems 1 – 3 in the guided notes.
Maximum
Minimum
Domain
Range
Period
Maximum
Minimum
Domain
Range
Period
Maximum
Minimum
Domain
Range
Period
1. f(t) = –3sin(t) 2.
3. f(t) = sin(5t)
4t
sin2)t(f
Calculating Periodicity• If f(t) = sin(bt), then period =
• Period is always positive
4. f(t) = sin(–6t) 5.
6.
|b|π2
4t
sin)t(f
4t3
sin)t(f
Your Turn:• Calculate the period of the following graphs:
7. f(t) = sin(3t) 8. f(t) = sin(–4t)
9. 10. f(t) = 4sin(2t)
11. 12.
5
t2sin6)t(f
8
tsin4)t(f
4t
sin)t(f
Amplitude• Amplitude is a trigonometric graph’s greatest distance
from the middle line. (The amplitude is half the height.)• Amplitude is always positive.
– If f(t) = a sin(t), then amplitude = | a |
2)tsin(21
)t(f
f(t) = 3sin(t) + 1
Calculating Amplitude Examples17. f(t) = 6sin(4t) 18. f(t) = –5sin(6t)
19. 20.)tsin(32
)t(f
3t
sin51
)t(f
Your Turn:• Complete problems 21 – 26 in the guided
notes
21. f(t) = –2sin(t) + 1 22. f(t) = sin(2t) + 4
23. f(t) = sin(2t) 24. f(t) = –3sin(t)
25. 26.
3t
sin3.0)t(f )t3sin(21
)t(f
Sketching Sine Graphs – Single Smooth Line!!!
