Matrix transformation doubt

For the first one, tan theta = 0 does not imply theta = 0, there is another possiblility.

You need to be thinking of the values of sin, cos, tan, in the full four quadrants.

Hmm... I was told that if you do sin theta/cos theta of those values you dont need to consider cos or sin

Then you were told wrong.

E.g. If tan theta = 0, then theta can be 0 or 180. Checking the values of the cosine will tell you wish one it is.

Im totally lost now.

Say if we forget about the whole tan theta stuff and stick to cos theta and sin theta,

for example in this worked example from this textbook:

cos theta = -root3/2 and sign theta = 1/2

Then the book says 'this occurs when theta is 150, therefore theta is in the second quadrant'.

Ive no idea where they get that its in the 'second quadrant', why are they using the result of cos inverse and not the sin one?

Thanks

Have you covered the CAST diagram?

Ive heard of it but havent covered it in great detail.

In that case check it out, textbook or Google. You really need it for working with inverse trig once you've got beyond the basic 0 to 90 degree angles where everything is positive. It will take a little while to pick up and appreciate, not just the quadrants, but also how to work the angles out.

In the case you've just presented, the fact that sine is positive and cosine is negative tells you it's in the second quadrant, and you can use either the sine or the cosine to work out which angle it is.

Is the cast diagram, where it tells you where each function is positive and in which quadrant? E.g. all of them are positive in the 1st one.

That's the one.

0.34 0.94
-0.94 0.34

I can do it straight off, tan theta = -47/17 hence theta = -70.1.... which is a clockwise rotation of 70.1 degrees. Why didnt I add 180? But adding 360 gives 289.9 degrees which is correct for an anti-clockwise rotation.

Well here you have the sine as negative and cosine as positive, and hence it's the 4th quadrant.

Last one. Read up on it.

Is it important to write A is an anticlockwise rotation of 41.41 degrees about O "FOLLOWED BY" an enlargement of SF 4 about O. My question is do you need to put it in that order or could it be the other way round?

Finally, how would I go about doing Q 8C on this paper:
http://store.aqa.org.uk/qual/gceasa/qp-ms/AQA-MFP1-W-QP-JUN08.PDF

Ive had a look at the mark scheme solution but I dont get how their solution works/ if theres an alternative.

Thanks.

Doesn't matter. Think about it; enlarge and then rotate, or rotate and then enlarge; you end up in the same place.



There's several ways.


1. Put the second transformation in matrix form, and multiply the two matrices together. You'd need to be familiar with the form of the reflection matrix for that, if it's not given.

2. Use simultaneous equations. Assume the matrix has entries a,b,c,d. Then you can see three points in the first figure that map to three points in the final figure and set up the equations (without actually doing it, I think you only need to use two of the points as that will give 4 equations.).