# Trigonometry

### Related Angles

###### Related Angles

2. Use of 90º, 180º, 270º and 360º

 90º and 270º 180º and 360º $$\sin (90 - \alpha) = \cos \alpha$$ $$\sin (90 + \alpha) = \cos \alpha$$ $$\sin (180 - \alpha) = \sin \alpha$$ $$\sin (180 + \alpha) = - \sin \alpha$$ $$\sin (270 - \alpha) = -\cos \alpha$$ $$\sin (270 + \alpha) = -\cos \alpha$$ $$\sin (360 - \alpha) = - \sin \alpha$$ $$\sin (360 + \alpha) = \sin \alpha$$ $$\cos (90 - \alpha) = \sin \alpha$$ $$\cos (90 + \alpha) = - \sin \alpha$$ $$\cos (180 - \alpha) = - \cos \alpha$$ $$\cos (180 + \alpha) = - \cos \alpha$$ $$\cos (270 - \alpha) = - \sin \alpha$$ $$\cos (270 + \alpha) = \sin \alpha$$ $$\cos (360 - \alpha) = \cos \alpha$$ $$\cos (360 + \alpha) = \cos \alpha$$ $$\tan (90 - \alpha) = \cot \alpha$$ $$\tan (90 + \alpha) = - \cot \alpha$$ $$\tan (180 - \alpha) = - \tan \alpha$$ $$\tan (180 + \alpha) = \tan \alpha$$ $$\tan (270 - \alpha) = \cot \alpha$$ $$\tan (270 + \alpha) = - \cot \alpha$$ $$\tan (360 - \alpha) = - \tan \alpha$$ $$\tan (360 + \alpha) = \tan \alpha$$

3. Bigger Angles

For bigger angles, we must find the remainder angles after multiplication of 360°.

Example

\begin{equation*} \begin{split} \sin 1470^{\text{o}} & = \sin (360^{\text{o}} \:.\: 4 + 30^{\text{o}}) \\\\ \sin 1470^{\text{o}} & = \sin 30^{\text{o}} \\\\ \sin 1470^{\text{o}} & = \frac{1}{2} \end{split} \end{equation*}

4. Negative Angles

Negative angles can be assumed that the angle is on the 4th quadrant.

$$\sin (- \alpha) = - \sin \alpha$$

$$\cos (- \alpha) = \cos \alpha$$

$$\tan (- \alpha) = - \tan \alpha$$