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F1 June 2018 question 10 help

this paper https://qualifications.pearson.com/content/dam/pdf/International%20Advanced%20Level/Mathematics/2013/Exam%20materials/WFM01_01_que_20170520.pdf
question 10 (e) how do i solve it
sorry i meant june 2017 paper but i have no idea how to edit the title
Original post by runballadmix


you should screen shot the entire question and post it because it will make it easier for people to help you.
(edited 5 years ago)
ee.JPGmy question is part e
Original post by runballadmix
/QUOTE]
i honestly dont know why but from trial and error i found out that
sin 75=sin 105
cos 75= -cos 105


what rotations do these matrix show?
@RDKGames
(edited 5 years ago)
matrix.PNG3.5KB
Original post by assassinbunny123

i honestly dont know why but from trial and error i found out that
sin 75=sin 105
cos 75= -cos 105


what rotations do these matrix show?
@RDKGames


Well those just come from the identities sin⁡θ≡sin⁡(180−θ)\sin \theta \equiv \sin(180-\theta) and cos⁡θ≡−cos⁡(180−θ)\cos \theta \equiv - \cos(180-\theta)

That matrix shows a clockwise rotation about the origin by 75 degrees.
Original post by runballadmix
my question is part e


The transformation T is a rotation by 105 degrees anticlockwise. This is denoted by

R=(cos⁡105−sin⁡105sin⁡105cos⁡105)\mathbf{R} = \begin{pmatrix} \cos 105 & -\sin 105 \\ \sin 105 & \cos 105 \end{pmatrix} ... (*)


But you also know that R=QP\mathbf{R} = \mathbf{Q} \mathbf{P}, therefore you can work out what it is with irrational matrix entries. ... (**)

Then, use (*) and (**) to equate the entries to one another. You should get numbers for sin⁡105\sin 105 and cos⁡105\cos 105

Use the appropriate identities to determine sin⁡75\sin 75 and cos⁡75\cos 75 from those two.
Original post by RDKGames
The transformation T is a rotation by 105 degrees anticlockwise. This is denoted by

R=(cos⁡105−sin⁡105sin⁡105cos⁡105)\mathbf{R} = \begin{pmatrix} \cos 105 & -\sin 105 \\ \sin 105 & \cos 105 \end{pmatrix} ... (*)


But you also know that R=QP\mathbf{R} = \mathbf{Q} \mathbf{P}, therefore you can work out what it is with irrational matrix entries. ... (**)

Then, use (*) and (**) to equate the entries to one another. You should get numbers for sin⁡105\sin 105 and cos⁡105\cos 105

Use the appropriate identities to determine sin⁡75\sin 75 and cos⁡75\cos 75 from those two.

thanks a lot

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