A few questions im not sure about

[ejf8888]

Hi,
There is one question on my spec homework that I cannot do and a couple that I have tried but am not sure about. Any help or suggestions are appreciated!

Thanks!

1) Write the equation for the graph that can also be described parametrically by x=2cos(t+1) and y=sin(t+1)

I have no idea about this one!

2) Find the magnitude of the shortest distance between the point (5,5) and the position vector i - 5j

I got 2 square root 29 as my answer but im not sure.

3) What is the range of f(x)= 3 - cosec(x)

[-1,1]

Thankyou in advance for any help!

[Over9000]

I shall try and answer this question, gimme a sec 

[TrueTears]

1)

and y = sin(t+1)
 

square both sides and add



so its an ellipse

[TrueTears]

the range of cosec(x) is R\[-1,1]

but here f(x) is being transformed, so we see it has a reflection in x axis and a vertical translation of 3 up

so the reflection doesn't change the range, it's still R\[-1,1]

how ever the translation of 3 up changes the whole graph (it moves it all 3 up)

so it would be R\[-1+3,1+3], therefore range is R\[2,4]

[Over9000]

For q.2, let the point [5,5], be represented by the position vector 5i + 5j
so we get distnace between the two is 5i + 5j -(i - 5j) = 4i + 10 j
Magnitude is is
So you are correct

[TrueTears]

lucky we didn't answer same Q over9000 lol was about to do that just then o.o

[Over9000]

yeh, lol 

[ejf8888]

Thankyou for your help!