Circular functions

[TrueTears]

I will skip a FEW steps here

b) Let and





But is not a subset of

therefore ran g is restricted to

dom g becomes [0,1]

therefore

c) let and







no restriction required as

so

[d0minicz]

thanks alot

but for b) which steps did you skip?
did it involve the 2 in front of sin^-1 (x)  ?

[TrueTears]

nah the 2 is meant to be in front of the I think i told you last time not to let my apologies lol, i thought it was a question where you had to simplify -_-

[d0minicz]

thanks man

can you pls show me the steps u take for solving the range
i tried subbing the domain into the equation but need some clarification through ur steps

thank you

[TrueTears]

b) The value that gives, then subbed back into cos(x) gives us the end points of the range.

and

subbing these in the cos(x) gives and

so the range is [-1,1]

[TrueTears]

part c) uses the same principle

the value of cos(x) subbed in gives the end points of the range

so and

and

so range is

[d0minicz]

oh i get it, thanks

for cos(tan^-1 x) how do i find the range when Dom = [0,oo) or R+ U {0}

[kamil9876]

tan^-1(x) for domain 0 to infinity gives a range of . So the range of this function is the same as the range of cos(u) where u has domain . THis gives a range of (0,1].

I see many people having problems with domain/range of composite functions, especially trig ones. Think of it as a computer/machine taking in numbers and spitting them out. So basically f(g(x)) takes some number x, then takes it through the machine g to produce a new number. Then takes that number and puts it through f. So in our case we're applying tan^-1 to numbers from 0 to infinity... producing numbers from 0 to pi/2 (but not including pi/2). Now all these numbers that belonged to that range are now inputed into the cosine function. And this gives numbers between 0 and 1. But not including 0 because cos(pi/2)=0 coz we didn't put pi/2 into our functions since it wasnt produced by tan^-1(x) earlier, just numbers very close to it.

[d0minicz]

ahhhhhhhhhh crap i overlooked the normal range of tan^-1 x ....
thanks kamil

[d0minicz]

The Questions 9, 10 and 11 in Exercise 3D essentials have been pissing me off for a long time lol
anywayz heres one

let where . Find in terms of two values of x in the range which satisfy each of the following equations.

a) tanx = -c

b) cotx = c

need alot of help understanding these questions
thanks alot !!!

anyone ?

[kamil9876]

http://vcenotes.com/forum/index.php/topic,11984.msg138611.html#msg138611

[d0minicz]

Simplify the following completely:
a)
b)

Prove the following :
a)
b)

thanks =]

[TrueTears]

The Questions 9, 10 and 11 in Exercise 3D essentials have been pissing me off for a long time lol
anywayz heres one

let where . Find in terms of two values of x in the range which satisfy each of the following equations.

a) tanx = -c

b) cotx = c

need alot of help understanding these questions
thanks alot !!!

anyone ?

Even better: http://vcenotes.com/forum/index.php/topic,9192.msg134547.html#msg134547

[TrueTears]

Simplify the following completely:
a)
b)

Prove the following :
a)
b)

thanks =]

a)
b)
c)
b) Too late I cbf typing this up, but same principle you see? gogo!

[d0minicz]

Couple of Q's guys...

1. equals:
A.
B.
C.
D.
E.

2. For and with and , equals to:

A. 0
B.
C.
D.
E.

Need to see workings for em

thanks !