Solve Trigonometric Equations with LaTeX: Step-by-Step Guide

[Zurtex]

I'm like writing my homework out on a computer and find LateX the easiest code to use (I have a fairly easy one at home but at college their maths editors are very limited)

I was going to use the preview post function to copy and paste everything into word but unfortunately it just stays the same no matter what I do (stuck on my first preview post). I am going to use and edit this thread for my homework but could someone please give a link of an online system where I can input LateX code and get a visual display of it.

1a) $${ \left[ \cos{ \frac{2 \pi}{5}} +i\sin{ \frac{2 \pi}{5}} \right] }^{10}$$

$$\cos{4\pi} + i\sin{4\pi} = 1$$

b) $${ \left[ \cos{\frac{\pi}{12}} + i\sin{\frac{\pi}{12}} \right] }^8$$

$$\cos{\frac{3\pi}{4}} + i\sin{\frac{3\pi}{4}} = \frac{\sqrt{2}}{2} + \frac{i\sqrt{2}}{2}$$

c) $${\left[ \cos{\left(-\frac{\pi}{27}\right)} + i\sin{\left(-\frac{\pi}{27}\right)} \right]}^9$$

$$\cos{\left(-\frac{\pi}{3}\right)} + i\sin{\left(-\frac{\pi}{3}\right)} = \frac{1}{2} - \frac{\sqrt{3}}{2}$$

d) $${\left( \cos{\frac{\pi}{18}} - i\sin{\frac{\pi}{18}} \right)}^3$$

$${\left( \cos{\left[-\frac{\pi}{18} \right]} + i\sin{\left[-\frac{\pi}{18}\right]} \right)}^3$$

$$\cos{\left[-\frac{\pi}{6}\right]} + i\sin{\left[-\frac{\pi}{6}\right]} = \frac{\sqrt{3}}{2} + \frac{i}{2}$$

2) $$z = 2(1 - i\sqrt{3})$$

$$z = 2 - i2\sqrt{3}$$

$$|z| = 4$$

$$arg(z) = -\frac{\pi}{3}$$

$$z^8 = \left[ 4 \left( \cos{\frac{\pi}{3}} + i\sin{\frac{\pi}{3}} \right) \right]^8$$

$$z^8 = 4^8 \left( \cos{\frac{8\pi}{3}} + i\sin{\frac{8\pi}{3}} \right)$$

$$z^8 = 65536 \left( -\frac{1}{2} + \frac{i\sqrt{3}}{2} \right)$$

$$z^8 = -16384 + i16384\sqrt{3}$$

$$\frac{1}{z^5} = z^{-5}$$

$$z^{-5} = \left[ 4 \left( \cos{\frac{\pi}{3}} + i\sin{\frac{\pi}{3}} \right) \right]^{-5}$$

$$z^{-5} = 4^{-5} \left( \cos{\frac{-5\pi}{3}} + i\sin{\frac{-5\pi}{3}} \right)$$

$$z^{-5} = \frac{1}{1024} \left( \frac{1}{2} + \frac{i\sqrt{3}}{2} \right)$$

$$z^{-5} = \frac{1}{2048} + \frac{i\sqrt{3}}{2048}$$

 

[arivero]

Zurtex, as LaTeX is free source software, you should be able to get a version of it for your platform, no need for online products, and no need for Word after all.

If you want to process LaTeX in a visual editor, you should look for non freee platforms such as SciTeX.

 

[Zurtex]

Originally posted by arivero
Zurtex, as LaTeX is free source software, you should be able to get a version of it for your platform, no need for online products, and no need for Word after all.

If you want to process LaTeX in a visual editor, you should look for non freee platforms such as SciTeX.

O.K thanks, well I'll set that up at home, however at college I have no rights to add or remove software.

 

[dlgoff]

I was going to use the preview post function to copy and paste everything into word but unfortunately it just stays the same no matter what I do (stuck on my first preview post). I am going to use and edit this thread for my homework but could someone please give a link of an online system where I can input LateX code and get a visual display of it.

Do a google search for "latex2rtf". I found a free latex to .rtf file program which can be read by word. But I haven't used it yet.

Regards

 

[Zurtex]

Originally posted by dlgoff
Do a google search for "latex2rtf". I found a free latex to .rtf file program which can be read by word. But I haven't used it yet.

Regards

Thanks, although I've never wrote anything in proper latex, I'm sure I'll find the correct teaching documents.