You are Here: Home >< Maths

# MAT Question watch

1. https://gyazo.com/509658f8e80ec97536c78a1322acac3b

I don't really understand the question and how to approach it. I also had trouble with eliminating x or y. This question is supposed to take 5 mins, if someone could take me through their approach to this question I would appreciate it.
2. (Original post by Louisb19)
https://gyazo.com/509658f8e80ec97536c78a1322acac3b

I don't really understand the question and how to approach it. I also had trouble with eliminating x or y. This question is supposed to take 5 mins, if someone could take me through their approach to this question I would appreciate it.
If you convert those simultaneous equations into matrix form then you have a rotation matrix for anticlockwise about the origin. There are two ways to view this, the simplest is that the determinant is always 1 so there exists an inverse matrix for all values of theta (though since the trig functions have period this is equivalent to ). So for all theta the equations have a unique solution.

Alternatively rotations are bijective. There must be a point mapping onto (2, 1) whatever is.

Disclaimer: No idea if this is right.
3. (Original post by 16Characters....)
If you convert those simultaneous equations into matrix form then you have a rotation matrix for anticlockwise about the origin. There are two ways to view this, the simplest is that the determinant is always 1 so there exists an inverse matrix for all values of theta (though since the trig functions have period this is equivalent to ). So for all theta the equations have a unique solution.

Alternatively rotations are bijective. There must be a point mapping onto (2, 1) whatever is.

Disclaimer: No idea if this is right.
I haven't read through this properly but it is not really suitable of the MAT. The best way to do this question is let sin(theta)=s and cos(theta)=c and treat like a usual simultaneous equation
4. (Original post by Gome44)
I haven't read through this properly but it is not really suitable of the MAT. The best way to do this question is let sin(theta)=s and cos(theta)=c and treat like a usual simultaneous equation
I tried doing that however I don't really understand what the 4 choices even mean.

I got something like 2c - s = x and something similar when eliminating y.

I don't get how this answers helps me towards making a choice.
5. (Original post by Louisb19)
I tried doing that however I don't really understand what the 4 choices even mean.

I got something like 2c - s = x and something similar when eliminating y.

I don't get how this answers helps me towards making a choice.
for every value of theta you get a unique value of x and y that solves the equations
6. (Original post by Gome44)
for every value of theta you get a unique value of x and y that solves the equations
Would it ever make sense that there could not be a value of theta which was invalid.

If the equation you formed was something like x = c/s could you say that there would be 1 value of theta ( theta = 0 ) in the interval which would not be valid?
7. (Original post by Louisb19)
Would it ever make sense that there could not be a value of theta which was invalid.

If the equation you formed was something like x = c/s could you say that there would be 1 value of theta ( theta = 0 ) in the interval which would not be valid?
yes

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: October 19, 2015
Today on TSR

### Exam Jam 2018

Join thousands of students this half term

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE