Trigonometry and Vector question?

[Timtasticle]

Hi, I am having trouble with this trigonometry question:

This is an inverse sine function:

g(x)= sin^-1(2x/x^2+1)

I have already worked out that:

a) g(√3)=π/3 and g(-√3)=-π/3

b) when g(x)=-π/4
x=-√2+1 or x=-√2-1

Now section c) says using the previous answer find:

i) The domain in exact values

ii) The range in exact values


I have also attached an image to this post with a vector question inside, help with that aswell would very much appreciated.

There is a diagram in the word doc to help but here is the vector question in text aswell:

Let OA =a, OC =c
CD: DB = p: q
Let OR = k1OD and CR = k2CA
Using the formula the formula OC + CR = OR find the values of k1 and k2 in terms of p and q

[Timtasticle]

Edit: sorry it should read for the vector question "OR=k1OD"

[TrueTears]

As requested:



Notice for the domain is thus for g(x) the domain is

Solving this inequality we can see that both sides of the inequality is true for all and hence the domain is just that.

Since

Let

Since u is a continuous function for all x we have

[Timtasticle]

Thanks a lot for the help

[evaever]

Let vector OA = a, vector OC = c
Lengths CD:DB = p:q
Let vector OR = k1OD and vector CR = k2CA
Using the formula the formula vectors OC + CR = vector OR find the values of k1 and k2 in terms of p and q.

Vector OR = (1-k2)c + k2a ... (1)

Vector OD = (1/(p+q))(qc+p vector OB) = (1/(p+q))(qc+p(a+c))

Vector OR = k1 vector OD = (k1/(p+q))(qc+p(a+c)) = k1c + (k1p/(p+q))a .............. (2)

Compare (1) and (2): 1-k2 = k1, k2 = k1p/(p+q)
Solve: k1 = (p+q)/(2p+q), k2 = p/(2p+q).