# Trigonometric Functions as Projections

## Similarity between sine and cosine functions

I'm sure you have noticed a strong similarity between sine and
cosine functions. This is hardly surprising since the definition of
sine is very similar to that of cosine. Use the applet below to
explore this as you plot sine (in blue)
and cosine (in green) on the same
axes. Then use the interactive to help with the exercises. (The applet
shows three full cycles to make it easier to see the similarity.)

## Exercises

- At what angles does \(\sin(\theta) = \cos(\theta)\)? What is the
value of \(\sin(\theta)\) and \(\cos(\theta)\) at these points?
- At what angles does \(\sin(\theta) = - \cos(\theta)\)?

## Challenge:

Look back on the earlier exercises you did for sine and cosine as
well as at the graph generated by the applet above. Can you express
mathematically the relationship between \(\sin(\theta)\) and
\(\cos(\theta)\)?