Practice Set 3
10 Strategic Questions
This set focuses on explaining transformations, reasoning with periodic models, comparing trig equations, and justifying solution sets.
Practice Questions
DOK 3 Practice Set: Trig Reasoning
Use Desmos strategically while you justify graph choices, compare periodic models, and explain why trig solutions make sense.
Question 1
A graph has amplitude 2, midline y = 1, and period 2π. Which equation matches it best?
Desmos Move: Match the coefficient for amplitude, the outside shift for midline, and the inside coefficient for period.
Question 2
A ferris wheel model has a maximum height of 42 feet and a minimum height of 10 feet. Which value should be the amplitude?
Desmos Move: Amplitude is half the distance between the highest and lowest values.
Question 3
On the interval 0° to 360°, which values solve sin(x) = cos(x)?
Desmos Move: Set the two trig values equal by using the unit circle or graph y = sin(x) and y = cos(x) together in degree mode.
Question 4
Why does y = -3 cos(x) + 2 start at y = -1 when x = 0?
Desmos Move: Evaluate the trig function at x = 0 instead of guessing from the shift alone.
Question 5
Which statement is true in Quadrant III?
Desmos Move: Use the signs of x- and y-coordinates on the unit circle to reason about trig signs.
Question 6
A trig graph has a maximum of 11 and a minimum of 3. What is its midline value?
Desmos Move: The midline is the average of the maximum and minimum values.
Question 7
A periodic model reaches a peak every 8 minutes. Which statement is best?
Desmos Move: When the context says the pattern repeats after a certain time, that value is the period.
Question 8
Which equation has the same amplitude as y = 4 sin(x) - 1 but a shorter period?
Desmos Move: Keep the amplitude coefficient the same, then change the inside coefficient to shorten the period.
Question 9
A graph oscillates around y = 5 between 1 and 9. Which statement is correct?
Desmos Move: The midline is halfway between the extreme values, and the amplitude is the distance from that line to a peak.
Question 10
Why is Desmos helpful when solving a simple trig equation like sin(x) = 0.6?
Desmos Move: Graph y = sin(x) and y = 0.6 together, then watch where they intersect on the interval you need.