Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Pick out the true statements:
(a) $|\sin z|≤1 ∀z∈\mathbb{C}$.
(b) $\sin^2z+\cos^2z=1 ∀z∈\mathbb{C}$.
(c) $\sin z =(e^{iz}-e^{-iz})/2 ∀z∈\mathbb{C}$.

(a) is not true for large z.
(b) true.
(c) true
Am I correct?

share|improve this question

2 Answers 2

(a) is not true but I don't know what you mean "large" $z$? I suppose you mean large in modulus? You can always use Liouville's Theorem of course for a more general result (or even the little Picard theorem for stronger results).

(c) is not true as you need a $i$ in the denominator.

(b) is true but you might want to prove it.

share|improve this answer

sin z cannot be bounded take z_n=in, then sin z_n=[Exp(-n)-Exp(n)]/2 this diverges to -infinity as n increases

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.