Trigonometry · Logic board
The Resonance Circuit
The observatory's orrery has gone dark. Its circuit board carries resonance from the source crystal to the core, but the conduits are twisted and five seals block the way. Route the wave and break every seal by reading its rhythm.
- 4 concepts
- 6 exercises
- About 5 minutes
- Before & after check
Built from the study material “Precalculus Ch. 4: Trigonometric Functions”. The lessons and exercises below come from that material. Upload your own notes to get a game like this one.
What you'll learn
Unit 1 · Angles and radians
Radian measure
The student can locate an angle in radians on the unit circle and convert between degrees and radians.
Unit 2 · Graphs of sine and cosine
Period of sin(bx) and cos(bx)
The student can compute the period of y = sin(bx) or cos(bx) and explain why a larger b shortens it.
Amplitude
The student can read the amplitude from an equation or graph and distinguish it from the peak-to-trough distance.
Unit 3 · Trigonometric equations
Solving sin(x) = k on [0, 2π)
The student can find every solution of a basic sine equation on one period.
Exercises
You'll meet these in order as you play. Each one uses the concept as the rule.
- Exercise 1LessonNot completed
The altar's rune line runs from 0 to 2π. Step onto 5π/6.
Radian measure
- Exercise 2LessonNot completed
The vault door's rings spin on y = sin(2t). Set the dial to one full period so the rings lock.
Period of sin(bx) and cos(bx)
- Exercise 3LessonNot completed
Four conduits hum on four different waves. Link each wave to how far it swings from its midline.
Amplitude
- Exercise 4LessonNot completed
The glyph door opens only if its planks show how to solve 2sin(x) = 1 on [0, 2π). One plank doesn't belong.
Solving sin(x) = k on [0, 2π)
- Exercise 5ReviewNot completed
The apprentice at the gate is stuck: why does a bigger b in y = sin(bx) make the period shorter? Explain it in your own words.
Period of sin(bx) and cos(bx)
- Exercise 6ChallengeNot completed
The Warden's shield spins on y = 3sin((π/2)t). Match its period to break through, and don't let the big swing fool you.
Period of sin(bx) and cos(bx) · Amplitude