y=−34 sin(10θ+10π)−14
I need to graph this trigonometry problem. I need the parent graph, period, vertical shift, phase shift, a separate graph showing the new mid line with the amplitude and a final product graph.
thanks for any help :)
parent is clearly sin(θ)
-34sin(10θ+10π) = -34sin(10(θ+π))
period is 2π/10
phase shift is -π
amplitude is 34
vertical shift is -14
midline is y = -14
see the graph at
To graph the trigonometric function y = -34sin(10θ + 10π) - 14, you can follow these steps:
1. Identify the parent graph: The parent graph for a sine function is y = sin(θ). It has an amplitude of 1, a period of 2π, and a midline of y = 0.
2. Period: The period of the function is determined by the coefficient of θ inside the sine function. In this case, the coefficient is 10, so the period is 2π/10 = π/5.
3. Vertical shift: The function is shifted downward by 14 units, so the new midline will be y = -14.
4. Phase shift: To find the phase shift, set the argument of the sine function (10θ + 10π) equal to zero and solve for θ:
10θ + 10π = 0
θ = -π
This means that the function is shifted to the left by π units.
5. Amplitude and Midline: The amplitude of the function is the absolute value of the coefficient in front of the sine function. In this case, it is |-34| = 34. The new midline is y = -14.
Now, let's create the graphs:
Graph 1 (Parent Graph):
The parent graph y = sin(θ) has an amplitude of 1 and a midline of y = 0. Draw a smooth sinusoidal curve between 0 to 2π.
Graph 2 (New Midline with Amplitude):
Shift the graph of the parent function downward by 14 units to get a new midline at y = -14. Draw a dashed line at y = -14. Then, draw a sinusoidal curve with an amplitude of 34 (peak and trough values) above and below the new midline.
Graph 3 (Final Product Graph):
To incorporate the phase shift, shift the graph from graph 2 horizontally to the left by π units. The amplitude and vertical shift remain the same.
Remember to label the axes, mark the key points on the graph (such as the highest and lowest points, x-intercepts, etc.), and indicate the period and amplitude on your graph.
By following these steps, you should be able to graph the trigonometric function y = -34sin(10θ + 10π) - 14.