Trigonometry Sheet 7
General Solutions of Trigonometric Equations
1. General Solutions $$1$$
Where $$n$$ is any integer ($$n \in \mathbb{Z}$$).
| Equation | General Solution ($$\theta$$) |
|---|---|
| $$\sin \theta = 0$$ | $$\theta = n\pi$$ |
| $$\cos \theta = 0$$ | $$\theta = (2n + 1)\frac{\pi}{2}$$ |
| $$\tan \theta = 0$$ | $$\theta = n\pi$$ |
2. General Solutions $$2$$
Where $$\alpha$$is the principal value and$$n \in \mathbb{Z}$$.
| Equation | General Solution ($$\theta$$) |
|---|---|
| $$\sin \theta = \sin \alpha$$ | $$\theta = n\pi + (-1)^n \alpha$$ |
| $$\cos \theta = \cos \alpha$$ | $$\theta = 2n\pi \pm \alpha$$ |
| $$\tan \theta = \tan \alpha$$ | $$\theta = n\pi + \alpha$$ |