Graph of Sine Function
Name______________________________
1. A function is a relationship that has exactly one output for each input.
In your graph what is the input - Angle or Sine Ratio?
In your graph what is the output - Angle or Sine Ratio?
2. Thinking back to the quadrants that you drew angles in,
Is the sine ratio positive or negative in the 1st quadrant?
Is the sine ratio positive or negative in the 3rd quadrant?
Is the sine ratio positive or negative in the 2nd quadrant?
Is the sine ratio positive or negative in the 4th quadrant?
3. Look at the graph. Is the function positive or negative when the angles were from the 1st quadrant?
Is the function positive or negative when the angles were from the 2nd quadrant?
Is the function positive or negative when the angles were from the 3rd quadrant?
Is the function positive or negative when the angles were from the 4th quadrant?
4. Look at the table of values on your graph and then the function.
Evaluate sin
π
Evaluate sin
6
π
Evaluate sin
4
π
3
Are the above ratios increasing or decreasing?
As the measure of the angles increase in the first quadrant is the function increasing or decreasing?
Evaluate sin
2π
3
Evaluate sin
7π
6
Evaluate sin
5π
3
Evaluate sin
3π
4
Evaluate sin
5π
4
Evaluate sin
7π
4
Evaluate sin
5π
6
Are the above ratios increasing or decreasing?
As the measure of the angles increase in the second quadrant is the function increasing or decreasing?
Evaluate sin
4π
3
Are the above ratios increasing or decreasing?
As the measure of the angles increase in the third quadrant is the function increasing or decreasing?
Evaluate sin
11π
6
Are the above ratios increasing or decreasing?
As the measure of the angles increase in the fourth quadrant is the function increasing or decreasing?
5. The table of values represents the points on the function: f
(θ ) = sin θ .
The five most important points are the following
below. Describe what the function is doing at these points
(0,0)
⎛π ⎞
⎜ ,1 ⎟
⎝2 ⎠
(π ,0)
⎛ 3π
⎞
⎜ , −1 ⎟
⎝ 2
⎠
( 2π ,0)
6. The amplitude is the distance from the maximum to an average value or the distance from the average value to a minimum.
Draw a line from a maximum value to the average value, in this case it is the x-axis, where the graph cycles, what is its
length?
7. As you can see from your graph the sine function repeats itself. The length of one cycle of called the period.
Starting at 0 when does the sine function complete one cycle?
8. Since the sine function can repeat itself indefinitely what is the domain?
9. Looking at your sine function what is the interval of its range using correct interval notation?
10. Finally, is the sine function even, odd, or neither? Explain.
Graph of Cosine Function
11. A function is a relationship that has exactly one output for each input.
In your graph what is the input - Angle or Cosine Ratio? What is the output - Angle or Cosine Ratio?
12. Thinking back to the quadrants that you drew angles in,
Is the cosine ratio positive or negative in the 1st quadrant? Positive or negative in the 2nd quadrant?
Is the cosine ratio positive or negative in the 3rd quadrant? Positive or negative in the 4th quadrant?
13. Look at the graph: Is the function positive or negative when the angles were from the 1st quadrant?
Is the function positive or negative when the angles were from the 2nd quadrant?
Is the function positive or negative when the angles were from the 3rd quadrant?
Is the function positive or negative when the angles were from the 4th quadrant?
14. Look at the table of values on your graph and then the function.
Evaluate cos
π
Evaluate cos
π
Evaluate cos
π
6
4
3
Are the above ratios increasing or decreasing?
As the measure of the angles increase in the first quadrant is the cosine function increasing or decreasing?
Evaluate cos
2π
3
Evaluate cos
7π
6
Evaluate cos
5π
3
Evaluate cos
3π
4
Evaluate cos
5π
4
Evaluate cos
7π
4
Evaluate cos
5π
6
Are the above ratios increasing or decreasing?
As the measure of the angles increase in the second quadrant is the cosine function increasing or decreasing?
Evaluate cos
4π
3
Are the above ratios increasing or decreasing?
As the measure of the angles increase in the third quadrant is the function increasing or decreasing?
Evaluate cos
11π
6
Are the above ratios increasing or decreasing?
As the measure of the angles increase in the fourth quadrant is the function increasing or decreasing?
15. The table of values represents the points on the function: f
(θ ) = cosθ .
The five most important points are the following
below. Describe what the function is doing at these points.
( 0,1)
⎛π ⎞
⎜ ,0⎟
⎝2 ⎠
(π , −1)
⎛ 3π ⎞
⎜ ,0⎟
⎝ 2 ⎠
( 2π ,1)
16. The amplitude is the distance from the maximum to an average value or the distance from the average value to a minimum.
Draw a line from a maximum value to the average value, in this case it is the x-axis. What is its length?
17. As you can see from your graph the cosine function repeats itself. The length of one cycle of called the period.
Starting at 0 when does the cosine function complete one cycle?
18. Since the cosine function can repeat itself indefinitely what is the domain?
19. Looking at your cosine function what is the interval of its range using correct interval notation?
20. Is the cosine function even, odd, or neither? Explain.