Precalc

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

  2. 1+tan⁡2θ=sec⁡2θ1+\tan^2\theta=\sec^2\theta

  3. sin⁡2θ=2sin⁡θcos⁡θ\sin2\theta=2\sin\theta\cos\theta

  4. sin⁡π6=12\sin\frac{\pi}{6}=\frac12

  5. cos⁡5π4=−12\cos\frac{5\pi}{4}=-\frac{1}{\sqrt2}

  6. tan⁡5π6=−13\tan\frac{5\pi}{6}=-\frac{1}{\sqrt3}

  7. tan⁡π=0\tan\pi=0

  8. sin⁡−1(−32)=−π3\sin^{-1}\left(-\frac{\sqrt3}{2}\right)=-\frac{\pi}{3}

  9. cos⁡(3π2)=0\cos\left(\frac{3\pi}{2}\right)=0

  10. cos⁡−1(−12)=3π4\cos^{-1}\left(-\frac{1}{\sqrt2}\right)=\frac{3\pi}{4}

  11. tan⁡−1(tan⁡5π4)=π4\tan^{-1}\left(\tan\frac{5\pi}{4}\right)=\frac{\pi}{4}

  12. sin⁡−1(sin⁡11π6)=−π6\sin^{-1}\left(\sin\frac{11\pi}{6}\right)=-\frac{\pi}{6}

  13. sin⁡(−3π2)=1\sin\left(-\frac{3\pi}{2}\right)=1

  14. cos⁡π=−1\cos\pi=-1

  15. An angle of 14π3\frac{14\pi}{3} radians is in Quandrant II

  16. An angle of 11π6\frac{11\pi}{6} radians is in Quandrant IV

  17. sec⁡(π2)\sec\left(\frac{\pi}{2}\right) is undefined

  18. sin⁡5π4=−12\sin\frac{5\pi}{4}=-\frac{1}{\sqrt2}

  19. csc⁡(3π2)=−1\csc\left(\frac{3\pi}{2}\right)=-1

  20. The period of y=sin⁡2θy=\sin2\theta is π\pi


  21. The period of y=cos⁡13θy=\cos\frac13\theta is 6π6\pi

  22. The period of y=tan⁡3θy=\tan3\theta is π3\frac{\pi}{3}

  23. π\pi radians is 180 degrees

  24. Working in Quandrant I sin⁡(tan⁡−1(x4))=xx2+16\sin\left(\tan^{-1}\left(\frac{x}{4}\right)\right)=\frac{x}{\sqrt{x^2+16}}