Question

Tan (x-y) if cos x= 1/√2 and siny = -2/√5, x is in Q4 and y is in Q3

Answer 1

you don't know quarter but you needn't it use the formul os tangen's sum

Answer 2

can you teach me how to solve problem like this? i 've got a lot of assignment like this. :)

Answer 3

There are a few trig rules which you can apply to these sorts of questions.

Firstly \(\cos^2 \theta +\sin^2 \theta = 1\) is always true.
Thus by knowing \(\cos x= 1/\sqrt{2}\) then you can determine \(\sin x = 1/\sqrt{2}\) (as \(\cos^2 x = 1/2\), so you then have \(0.5+\sin^2 x=1\) giving you \(\sin x\). In the same way you can find \(\cos y\) from knowing \(\sin y\).

Secondly, \[\tan \theta = \frac{\sin \theta}{\cos \theta}\] so you can work out what \( \tan x\) and \(\tan y\) are, given the above.

Thirdly there are a number of addition formulae in trigonometry. In this case \[\tan (x+y)=\frac{\tan x +\tan y}{1-\tan x \tan y}\] where you know these from the second step.

There are other addition formulae which you can find here http://mathworld.wolfram.com/TrigonometricAdditionFormulas.html which might help you with your other questions.
Hope this helps.