Real World: Waves and Oscillations

Calculus Readiness · Axiom Academy

Trigonometry in the Real World Sine, cosine, and tangent leave the classroom — they measure a tower you can't reach, ride a Ferris wheel, and model a day of your own body temperature. Three places the same trig shows up: a tower you measure from the ground , a Ferris wheel that repeats every 60 seconds , and the 24-hour rhythm of your own body — do each one and watch the math drive it. You stand 80 m from the base of a cell tower and sight the top. You can't climb it — but you can measure the angle of elevation . Drag that angle and watch the height fall out of . A Ferris wheel of radius 20 m , centre 22 m up, turns once every 60 s . You board at the bottom. Drag time forward and watch your height trace a wave: . Your body temperature rises and falls over a day — a sinusoid: . Drag the amplitude A and watch the whole 24-hour curve swing wider or flatter around its midline. One toolkit, three jobs: a triangle measures what you can't reach, and a sinusoid models anything that repeats. The Ferris wheel, your body clock, a 440 Hz piano note , and the 120 V from your wall socket are all the same wave with different numbers — which is why this unit shows up in every technical field.

This is the written version of the interactive lesson above. See the full Calculus Readiness course.