Basic Trig Identities


Next let's see how these functions are related. In the video, we explain the following identities:

  1. $\sin(\frac{\pi}{2}-\theta)=\cos(\theta)$

  2. $\cos(\frac{\pi}{2}-\theta)=\sin(\theta)$

  3. $\sin(-\theta)=-\sin(\theta)$

  4. $\cos(-\theta)=+\cos(\theta)$

  5. $\sin(\frac{\pi}{2}+\theta)=\cos(\theta)$

  6. $\cos(\frac{\pi}{2}+\theta)=-\sin(\theta)$

  7. $\sin^2(\theta)+\cos^2(\theta)=1$

  8. $\tan^2(\theta)+1=\sec^2(\theta)$

  9. $1+\cot^2(\theta)=\csc^2(\theta)$


The last three are called Pythagorean identities, since they're all based on the Pythagorean theorem.