Graphs of Sine & Cosine — Drills
Graphs of Sine & Cosine has 6 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 8 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Coefficient — The number multiplying a variable — the 3 in 3n.
- π — The circumference of any circle divided by its diameter — about 3.14159.
- Radius — Centre to edge. Half the diameter.
- Sine — sin θ = oppositehypotenuse.
- Amplitude — Half the distance from the top to the bottom — how tall the wave is.
- Period — How long before the pattern repeats.
- Midline — The horizontal line halfway between the peaks and troughs.
- Phase shift — A horizontal slide — how far the wave has been moved sideways.
Amplitude
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Give the amplitude of y=-3sin x.
Worked answer
3
|-3|=3
Problem 2
Give the amplitude of y=5sin x.
Worked answer
5
|5|=5
Period
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Give the period of y=sin(2x) as a multiple of π. Enter just the number or fraction.
Worked answer
1
2π2
=1π
Problem 2
Give the period of y=sin(4x) as a multiple of π. Enter just the number or fraction.
Worked answer
1/2
2π4
=1/2π
Midline
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A wave peaks at 27 and bottoms at 17. Give its midline as a number.
Worked answer
22
27+172=22
Problem 2
A wave peaks at 10 and bottoms at 2. Give its midline as a number.
Worked answer
6
10+22=6
Amp2
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A wave peaks at 28 and bottoms at 16. Find its amplitude.
Worked answer
6
28-162=6
Problem 2
A wave peaks at 10 and bottoms at 0. Find its amplitude.
Worked answer
5
10-02=5
Maxmin
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the minimum of y=3sin x+8.
Worked answer
5
Midline 8, amplitude 3
8 - 3 = 5
Problem 2
Find the maximum of y=5sin x+6.
Worked answer
11
Midline 6, amplitude 5
6 + 5 = 11
Wheel
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A Ferris wheel of radius 20 m has its centre 27 m above the ground. How high is the lowest point?
Worked answer
7
27-20=7
Problem 2
A Ferris wheel of radius 25 m has its centre 31 m above the ground. How high is the lowest point?
Worked answer
6
31-25=6