Circular Functions and Transformations
Use the unit circle to understand sine, cosine and tangent graphs, then transform them.
Unit-circle definitions
For an angle \(\theta\), the point on the unit circle has coordinates
\[(\cos\theta,\sin\theta).\]
Graph transformations
For a function such as
\[y=a\sin(b(x-c))+d,\]
- \(|a|\) controls amplitude.
- \(\frac{2\pi}{|b|}\) controls period, if using radians.
- \(c\) gives horizontal shift.
- \(d\) gives vertical shift.