PredictionTrigonometryMedium
The Sine–Cosine Clock
Pick any angle, divide sin by cos of its complement — the answer is always one.
Worked demonstration
Pick any angle x between 1° and 89° (say 68°). Work out sin(x). Then work out cos(90° − x). Divide the first result by the second. What number do you always get?
Try it yourself
Why it works
cos(90° − x) equals sin(x) for every angle (they are cofunctions), so sin(x) ÷ cos(90° − x) = 1 always.
Background & Explore Further
The cofunction identity and SOH-CAH-TOA drive surveying, signal processing and the sine waves behind sound and light. Explore why sine and cosine mirror across 45°.
Maths Made Magic — Queen Mary University of London (cs4fn)