Calculus for Team-Based Inquiry Learning: PREVIEW Edition — Instructor Version

Appendix B List of Trigonometric Identities

1. ${\displaystyle [\sin (\alpha ){]}^2+[\cos (\alpha ){]}^2=1}$
2. ${\displaystyle \cos (\alpha +\beta )=\cos (\alpha )\cos (\beta )-\sin (\alpha )\sin (\beta )}$
3. ${\displaystyle \sin (\alpha +\beta )=\sin (\alpha )\cos (\beta )+\cos (\alpha )\sin (\beta )}$
4. ${\displaystyle \cos (2\alpha )=[\cos (\alpha ){]}^2-[\sin (\alpha ){]}^2=2[\cos (\alpha ){]}^2-1=1-2[\sin (\alpha ){]}^2}$
5. ${\displaystyle \sin (2\alpha )=2\sin (\alpha )\cos (\alpha )}$
6. ${\displaystyle [\cos (\alpha ){]}^2={\displaystyle \frac{1+\cos (2\alpha )}{2}}}$
7. ${\displaystyle [\sin (\alpha ){]}^2={\displaystyle \frac{1-\cos (2\alpha )}{2}}}$
8. ${\displaystyle \sin (\alpha )\cos (\beta )={\displaystyle \frac{\sin (\alpha +\beta )+\sin (\alpha -\beta )}{2}}}$
9. ${\displaystyle \sin (\alpha )\sin (\beta )={\displaystyle \frac{\cos (\alpha -\beta )-\cos (\alpha +\beta )}{2}}}$
10. ${\displaystyle \cos (\alpha )\sin (\beta )={\displaystyle \frac{\sin (\alpha +\beta )-\sin (\alpha -\beta )}{2}}}$
11. ${\displaystyle \cos (\alpha )\cos (\beta )={\displaystyle \frac{\cos (\alpha -\beta )+\cos (\alpha +\beta )}{2}}}$
12. ${\displaystyle \sin (\alpha )+\sin (\beta )=2\sin \left({\displaystyle \frac{\alpha +\beta }{2}}\right)\cos \left({\displaystyle \frac{\alpha -\beta }{2}}\right)}$
13. ${\displaystyle \sin (\alpha )-\sin (\beta )=2\cos \left({\displaystyle \frac{\alpha +\beta }{2}}\right)\sin \left({\displaystyle \frac{\alpha -\beta }{2}}\right)}$
14. ${\displaystyle \cos (\alpha )+\cos (\beta )=2\cos \left({\displaystyle \frac{\alpha +\beta }{2}}\right)\cos \left({\displaystyle \frac{\alpha -\beta }{2}}\right)}$
15. ${\displaystyle \cos (\alpha )-\cos (\beta )=-2\sin \left({\displaystyle \frac{\alpha +\beta }{2}}\right)\sin \left({\displaystyle \frac{\alpha -\beta }{2}}\right)}$