Where Sine Meets Cosine

Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 9 of 51.

Draw the sine and cosine graphs on one axis and they cross twice in every lap. At a crossing the point on the unit circle is as high as it is far to the right: sin x = cos x. Sine and cosine are never 0 at the same angle, so you may divide by cos x, which gives tan(x) = 1.

$Sine and cosine between 0 and 360 degrees, crossing twice$

On the circle, height equals x on the line through the centre at 45°. It meets the circle at 45° and at the opposite point, 225°. So in one lap the graphs cross at 45° and 225°, and they cross again 360° after each of those.

Challenge

This time the interval is in radians. Tap every angle in it on the goal row where the sine and cosine graphs cross, where tan(theta) = 1. Press Check.