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Solving Strategy
- Isolate the trig function
- Find the reference angle
- Use unit circle for all solutions in [0, 2π)
- For general solutions, add period multiples
General Solutions
sinθ=k: θ=arcsin(k)+2nπ or θ=(π−arcsin(k))+2nπ
cosθ=k: θ=±arccos(k)+2nπ
tanθ=k: θ=arctan(k)+nπ
Multiple Angles
For sin(nx)=k: solve for u=nx on [0, 2nπ), then divide by n.
Inverse Trig Functions
| Function | Domain | Range |
|---|
| arcsin(x) | [−1, 1] | [−π/2, π/2] |
| arccos(x) | [−1, 1] | [0, π] |
| arctan(x) | (−∞,∞) | (−π/2, π/2) |
Key Tips
- Factor, do not divide by trig functions
- Use identities to reduce to one trig function
- Check solutions in original equation
- For compositions like sin(arccos x), draw a right triangle