Example: Intersection of sine and cosine  Graphs of trig functions  Trigonometry  Khan Academy  Summary and Q&A
TL;DR
The graphs of y=sin(theta) and y=cos(theta) intersect twice between 0 and 2pi.
Questions & Answers
Q: How many times do the graphs of sine and cosine intersect between 0 and 2pi?
The graphs of sine and cosine intersect twice between 0 and 2pi.
Q: What are the coordinates of the points where the graphs intersect?
The first intersection point is approximately (sqrt(2)/2, sqrt(2)/2), and the second intersection point is approximately (sqrt(2)/2, sqrt(2)/2).
Q: What are the values of cosine and sine at theta=0?
At theta=0, cosine is equal to 1 and sine is equal to 0.
Q: What are the values of cosine and sine at theta=pi/2?
At theta=pi/2, cosine is equal to 0 and sine is equal to 1.
Summary & Key Takeaways

The graph of y=cos(theta) intersects the yaxis at 1 (theta=0) and 1 (theta=pi and 2pi), forming a curve that oscillates between these points.

The graph of y=sin(theta) intersects the xaxis at 0 (theta=0 and 2pi) and 1 (theta=pi), forming a similar oscillating curve.

Between 0 and 2pi, the two graphs intersect at two points, approximately between 0 and pi/2 and between pi and 3pi/2.