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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: The Detective on February 28, 2010, 11:54:16 am

Title: Things to memorize in methods :]
Post by: The Detective on February 28, 2010, 11:54:16 am: Hi everyone, I know for methods there are a few solutions you have to remember like tan30. Just wondering if someone could provide a list of them that would be very helpful :) thanks
Title: Re: Things to memorize in methods :]
Post by: the.watchman on February 28, 2010, 11:59:06 am: $\sin {0} = 0$

$\sin {\frac{\pi}{6}} = \frac{1}{2}$

$\sin {\frac{\pi}{3}} = \frac{\sqrt{3}}{2}$

$\sin {\frac{\pi}{4}} = \frac{\sqrt{2}}{2}$

$\sin {\frac{\pi}{2}} = 1$

$\cos {0} = 1$

$\cos {\frac{\pi}{6}} = \frac{\sqrt{3}}{2}$

$\cos {\frac{\pi}{3}} = \frac{1}{2}$

$\cos {\frac{\pi}{4}} = \frac{\sqrt{2}}{2}$

$\cos {\frac{\pi}{2}} = 0$

$\tan {0} = 0$

$\tan {\frac{\pi}{6}} = \frac{\sqrt{3}}{3}$

$\tan {\frac{\pi}{3}} = \sqrt{3}$

$\tan {\frac{\pi}{4}} = 1$

$\tan {\frac{\pi}{2}} = undef.$
Title: Re: Things to memorize in methods :]
Post by: appianway on February 28, 2010, 12:03:45 pm: You can derive most of those if you need to though.
Title: Re: Things to memorize in methods :]
Post by: the.watchman on February 28, 2010, 12:07:54 pm: Yep, you can use:

1) A right-angled isosceles triangle of side length 1,1, $\sqrt{2}$ (angles of $\frac{\pi}{4}$ )

2) An equilateral triangle cut in half - right-angled triangle of side length $\sqrt{3}$ ,1,2 (angles of $\frac{\pi}{6}$ and $\frac{\pi}{3}$
Title: Re: Things to memorize in methods :]
Post by: The Detective on February 28, 2010, 12:20:20 pm: Okay thanks very much both of you! I'll refer back to these during the year ;D
Title: Re: Things to memorize in methods :]
Post by: superflya on February 28, 2010, 07:01:58 pm: memorising just the sin values, u automatically know the cos using sin 30 = cos 60 , sin 60 =cos30 , sin45 = cos 45 but sin 0= 0 and cos 0=1. oh and sin90=1 whereas cos90=0. these have no relations with tan though.
Title: Re: Things to memorize in methods :]
Post by: the.watchman on February 28, 2010, 07:07:38 pm: Quote from: superflya on February 28, 2010, 07:01:58 pm
memorising just the sin values, u automatically know the cos using sin 30 = cos 60 , sin 60 =cos30 , sin45 = cos 45 but sin 0= 0 and cos 0=1. oh and sin90=1 whereas cos90=0. these have no relations with tan though.

For the others, try to visualise the trig graphs, then the values are a dead giveaway
Title: Re: Things to memorize in methods :]
Post by: olly_s15 on February 28, 2010, 08:27:13 pm: Quote from: superflya on February 28, 2010, 07:01:58 pm
memorising just the sin values, u automatically know the cos using sin 30 = cos 60 , sin 60 =cos30 , sin45 = cos 45 but sin 0= 0 and cos 0=1. oh and sin90=1 whereas cos90=0. these have no relations with tan though.

They do have relations with tan. Tan30= sin30/cos30 etc...
Title: Re: Things to memorize in methods :]
Post by: the.watchman on February 28, 2010, 08:29:04 pm: Quote from: olly_s15 on February 28, 2010, 08:27:13 pm
Quote from: superflya on February 28, 2010, 07:01:58 pm
memorising just the sin values, u automatically know the cos using sin 30 = cos 60 , sin 60 =cos30 , sin45 = cos 45 but sin 0= 0 and cos 0=1. oh and sin90=1 whereas cos90=0. these have no relations with tan though.

They do have relations with tan. Tan30= sin30/cos30 etc...

Absolutely, you can derive the tan formulas from the rest.
However, as in all cases, it is better to try to memorise them.
Title: Re: Things to memorize in methods :]
Post by: superflya on February 28, 2010, 08:47:02 pm: Quote from: olly_s15 on February 28, 2010, 08:27:13 pm
Quote from: superflya on February 28, 2010, 07:01:58 pm
memorising just the sin values, u automatically know the cos using sin 30 = cos 60 , sin 60 =cos30 , sin45 = cos 45 but sin 0= 0 and cos 0=1. oh and sin90=1 whereas cos90=0. these have no relations with tan though.

They do have relations with tan. Tan30= sin30/cos30 etc...

true, i just stated the ones that u can remember with very little effort.