Talk:Trigonometry/Sine Squared plus Cosine Squared

Validity beyond Reals
Note to more advanced users: when considering the sin and cos of complex numbers, sin and cos may take any values; however, this formula remains true.


 * I think this note should move to book two and be expanded there. It would be good as an exercise with hints there ...

Use the formula for sin and cosine in terms of exponentials.
 * is $$\displaystyle\cos(x)=4$$ possible for $$x\in \mathbb{C}$$?
 * is $$\displaystyle\cos(x)=i$$ possible for $$x\in \mathbb{C}$$?
 * is $$\displaystyle\sin^2(x)+\cos^2(x)=1$$ for all $$x\in \mathbb{C}$$?

JamesCrook (talk) 17:17, 3 December 2010 (UTC)


 * OK, I agree to this.--Wisden (talk) 18:49, 4 December 2010 (UTC)