# Tagged Questions

2answers
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### Express $\sin 3\theta$ and $\cos 3\theta$ as functions of $\sin \theta$ and $\cos \theta$ using Euler's identity

Using Euler's identity ($e^{in\theta}=\cos n\theta+i \sin n\theta$), express $\sin 3\theta$ and $\cos 3\theta$ as functions of $\sin \theta$ and $\cos \theta$. Any ideas?
1answer
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1answer
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### Finding modulus and argument of z³ - 4√3 + 4i = 0

I think I am messing up somewhere as the principle argument should be a nice number from the standard triangles such as $\fracπ4$, $\fracπ3$ or $\fracπ6$ or something close. (That's what we have ...
3answers
356 views

### Find all complex solutions of $\sin(z)=1$ [closed]

Find all complex solutions of $\sin(z)=1$. How would I go about this?
1answer
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### Trigonometry and complex numbers

Suppose $z_0=e^{i\theta_0}$ a complexe number as $\theta_0\in ]-\pi,\pi[ \setminus\{0\}$. For $n\in \mathbb{N}$, we pose $z_{n+1}=\dfrac{|z_n|+z_n}{2}$ and $z_n=r_ne^{i\theta_n}$ with ...
1answer
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### Trigonometry with complex numbers [closed]

Express $(\cos(x))^5$ in terms of cosines of multiples of $x$. I've racked my brains for ages on this one! No notes to help me out, and I've failed to find any help online.
3answers
483 views

### Is it true that $|\sin^2z+\cos^2z|=1, \forall z \in\Bbb C$?

We know that equation $\sin^2z+ \cos^2z=1$ which holds $\forall z \in\Bbb R$, actually holds $\forall z \in\Bbb C$. Is it true that $|\sin^2z+\cos^2z|=1, \forall z \in\Bbb C$? Thanks in ...