Precalc

  1. \sin^2\theta+\cos^2\theta=1

  2. 1+\tan^2\theta=\sec^2\theta

  3. \sin2\theta=2\sin\theta\cos\theta

  4. \sin\frac{\pi}{6}=\frac12

  5. \cos\frac{5\pi}{4}=-\frac{1}{\sqrt2}

  6. \tan\frac{5\pi}{6}=-\frac{1}{\sqrt3}

  7. \tan\pi=0

  8. \sin^{-1}\left(-\frac{\sqrt3}{2}\right)=-\frac{\pi}{3}

  9. \cos\left(\frac{3\pi}{2}\right)=0

  10. \cos^{-1}\left(-\frac{1}{\sqrt2}\right)=\frac{3\pi}{4}

  11. \tan^{-1}\left(\tan\frac{5\pi}{4}\right)=\frac{\pi}{4}

  12. \sin^{-1}\left(\sin\frac{11\pi}{6}\right)=-\frac{\pi}{6}

  13. \sin\left(-\frac{3\pi}{2}\right)=1

  14. \cos\pi=-1

  15. An angle of \frac{14\pi}{3} radians is in Quandrant II

  16. An angle of \frac{11\pi}{6} radians is in Quandrant IV

  17. \sec\left(\frac{\pi}{2}\right) is undefined

  18. \sin\frac{5\pi}{4}=-\frac{1}{\sqrt2}

  19. \csc\left(\frac{3\pi}{2}\right)=-1

  20. The period of y=\sin2\theta is \pi

  21. The period of y=\cos\frac13\theta is 6\pi

  22. The period of y=\tan3\theta is \frac{\pi}{3}

  23. \pi radians is 180 degrees

  24. Working in Quandrant I \sin\left(\tan^{-1}\left(\frac{x}{4}\right)\right)=\frac{x}{\sqrt{x^2+16}}