Grade 12 Radians Quiz

In the land of Truffula Trees, a Sneetch needs to turn exactly 45 degrees to find the hidden star. If the Sneetches use radians instead of degrees, how much would that be?

• 0.7854

• 3.1416

• 2.3562

• 1.5708

Imagine you're a bird, flying high and free. You've flown π/3 radians of your circular path. How many degrees, my dear, have you flown, you see?

• 30

• 60

• 180

• 45

In the land of Whoville, there's a circle so fine, with a radius of 5, it's as perfect as a line. If the central angle is as sweet as a pea, being π/3, oh what could the arc length be?

• 25π/3

• 10π/3

• 5π/3

• 2π/3

Imagine you're a bird, flying high and free, and you spot a circular nest, oh what a sight to see! The nest has a radius of 8, and you see a tasty worm on an arc, with a central angle, as big as 2π/3, do you see? How long is the arc, where the worm does be?

• 4π/3

• 12π/3

• 8π/3

• 16π/3

In the land of Truffula Trees, a Sneetch is trying to measure the angle of the sun at π/6 radians. Can you help him find the value of tan(π/6)?

• 1/√3

• 0

• 1

• √3

Imagine, if you will, a wheel spinning with glee, at 2 radians per second, as fast as can be! Now, if this wheel's radius measures 4 meters, oh so tall, what's the speed of a point on its edge, after all?

• 16 m/s

• 2 m/s

• 5 m/s

• 8 m/s

Imagine, my friend, a big wheel in the sky, as tall as a 20 meter high pie. It spins all around, not making a sound, completing one full turn in just 30 seconds, oh my! Can you tell, oh so swell, the angular velocity of this Ferris wheel, in radians per second, do tell?

• 40 radians per second

• 0.05 radians per second

• 2.5 radians per second

• 0.21 radians per second