Basic Trig Identities
Next let's see how these functions are related. In the video, we
explain the following identities:
- $\sin(\frac{\pi}{2}-\theta)=\cos(\theta)$
- $\cos(\frac{\pi}{2}-\theta)=\sin(\theta)$
- $\sin(-\theta)=-\sin(\theta)$
- $\cos(-\theta)=+\cos(\theta)$
- $\sin(\frac{\pi}{2}+\theta)=\cos(\theta)$
- $\cos(\frac{\pi}{2}+\theta)=-\sin(\theta)$
- $\sin^2(\theta)+\cos^2(\theta)=1$
- $\tan^2(\theta)+1=\sec^2(\theta)$
- $1+\cot^2(\theta)=\csc^2(\theta)$
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The last three are called Pythagorean identities, since they're
all based on the Pythagorean theorem.
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