Radians & the Unit Circle — Drills
Radians & the Unit Circle has 5 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 13 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.
- Arc — Part of the edge; a "pizza slice" bounded by two radii.
- Sine — sin θ = oppositehypotenuse.
- Cosine — cos θ = adjacenthypotenuse.
- Central angle — An angle whose vertex is the centre. Equal to its arc.
- Radian — The angle whose arc length equals the radius. A full turn is 2π radians.
- Unit circle — The circle of radius 1 centred at the origin.
- Reference angle — The acute angle between the terminal side and the x-axis.
- x-coordinate — The first number — how far across.
- y-coordinate — The second number — how far up or down.
- Quadrant — One of the four regions the axes divide the plane into.
Todeg
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Convert 2π3 radians to degrees.
Worked answer
120
2 × 1803=120
Problem 2
Convert 5π6 radians to degrees.
Worked answer
150
5 × 1806=150
Reference
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the reference angle for 135°.
Worked answer
45
180-135=45
Problem 2
Find the reference angle for 210°.
Worked answer
30
210-180=30
Coterminal
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the angle between 0° and 360° coterminal with 647°.
Worked answer
287
647-360=287
Problem 2
Find the angle between 0° and 360° coterminal with 395°.
Worked answer
35
395-360=35
Cotermneg
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the angle between 0° and 360° coterminal with -71°.
Worked answer
289
-71+360=289
Problem 2
Find the angle between 0° and 360° coterminal with -152°.
Worked answer
208
-152+360=208
Arc
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A circle of radius 4 has a central angle of 2 radians. Find the arc length.
Worked answer
8
4 × 2 = 8
Problem 2
A circle of radius 7 has a central angle of 2.5 radians. Find the arc length.
Worked answer
17.5
7 × 2.5 = 17.5