MathCastle
TrigonometrySuperchallengeGraphs of Sine and Cosine

Graphs of Sine and Cosine · Superchallenge problem

For how many ordered pairs (a,b)(a,b) of integers with 1≤a≤101\le a\le10 and 1≤b≤101\le b\le10 does y=sin⁡(ax)+cos⁡(bx)y=\sin(ax)+\cos(bx) have fundamental (smallest positive) period exactly 2π2\pi?