Solve Cosec x Graph Transformations: Alternative Method without Substitution"

[bobbricks]

Question 4b: http://www.skinners-maths.co.uk/specimen A level papers/EC3paper/EC3sh_H.pdf

I wrote out that (1)(a+b)=1 and (-5)(a+b)=-1 but that doesn't seem to work? I know you can solve it directly by substituting in the co ordinates from the graph, but is there an alternative to doing this question using the fact that the cosecx graph has been translated/stretched from (pi/2, 1) to (pi/2,-1) and (3pi/2,-1) to (3pi/2,-5).

 

[Mark44]

Question 4b: http://www.skinners-maths.co.uk/specimen A level papers/EC3paper/EC3sh_H.pdf

I wrote out that (1)(a+b)=1 and (-5)(a+b)=-1 but that doesn't seem to work?

It doesn't seem to work because both equations are incorrect.

You have the function's formula, and from the graph you are given
-1 = f($\pi/2$), and -5 = f($3\pi/2$).
Substitute the formula for your function, and you should get two equations in the unknowns a and b.

I know you can solve it directly by substituting in the co ordinates from the graph, but is there an alternative to doing this question using the fact that the cosecx graph has been translated/stretched from (pi/2, 1) to (pi/2,-1) and (3pi/2,-1) to (3pi/2,-5).

You can look at it this way, but I don't think it's helpful to do so. Problem 4b asks only that you find a and b.