VCE Specialist 3/4 Question Thread!

[motocross53]

could someone please show me how to do this,
4.4 Q5a of essential book:

show that sin(theta)+cos(theta)i=cis(pi/2-theta)

thanks

as required

sorry mate,
i still dont really following you,
could you please give a longer explanation

[nubs]

as required

To do a 'show that' question, you need to pick a side, and adjust it and manipulate it so that it equals the other side. so pick the left hand side, or right hand side (whichever you think is easier to manipulate and work on). Tony picked the RHS, which he then manipulated to = the LHS, so he did this:
RHS = (He then proceed to expand this)

Remember:


So

Also remember that, and

So, = LHS

[rife168]

Complex number question: (From VCAA 2006 Exam 1)

Solve the quadratic equation , expressing your answers in exact cartesian form.

[abd123]

Complex number question: (From VCAA 2006 Exam 1)

Solve the quadratic equation , expressing your answers in exact cartesian form.

In polar form:

Hence,

Let , 

Therefore,

let

.

Thus, .

You can also use , Where a, b holds r.

Hoped I Helped .

[kensan]

Must be a gap in my knowledge here, but from

and when you square rooted doesn't the argument change?
I'm confused because when you subbed in k=0, you got
but wouldn't it be   because 
If that makes sense haha
Also I was looking through my textbook and couldn't find any examples of this type of question, is this assumed after all knowledge learnt?

[rife168]

Must be a gap in my knowledge here, but from

and when you square rooted doesn't the argument change?
I'm confused because when you subbed in k=0, you got
but wouldn't it be   because 
If that makes sense haha
Also I was looking through my textbook and couldn't find any examples of this type of question, is this assumed after all knowledge learnt?

When he wrote
the next line should have been

Hope that clears it up. Also, this is a VCAA past exam question, so it would be good to make sure you understand it fully.

[kensan]

Ah I see, opposite of De Moivre's theorem.
Thanks man

[monkeywantsabanana]

Why is this invalid?

= =

[nubs]

Let a = 2i+j-k
Let b = i+j+k

Using these values, find ((a-b).(a-b))^(1/2)

Now find (a-b)

What does that tell you?

Remember that a.a doesn't equal a^2, it equals |a|^2

Similarly, (a-b).(a-b) doesn't equal (a-b)^2, it equals |a-b|^2
So ((a-b).(a-b))^(1/2) = |a-b|

[paulsterio]

= =

Nirbaan explained it, but in simple terms, DOES NOT EQUAL

in fact, =

[TrueTears]

Why is this invalid?

= =

Well firstly consider this statement

Is "squaring" defined for a vector? There is no distinct "multiplication" operation defined for a vector in your usual sense.

[monkeywantsabanana]

Ah ok thanks!

[powerrrr]

Hi, I'm having a bit of trouble with De Moivre's...

If W = 54rt2 cis (3pi/4), find solutions to cuberootW

I only got one solution which is 3rt2cis pi/4

Can someone help please? There's 2 more..

[trinh]

, k ∈ Z
, k ∈ Z

Sub in k=-1, 0 and 1 to get:


You pretty much just forgot to add on the in step 2, hence missing out on the other two solutions

[claireb]

Having a mental block and can't seem to work out these questions (tech free)

edit:
- cos^2(x)/sin(x) + sin(x)  answer=cosec(x)

- Simplify tan((pi/2)-y)    answer= cot(y)
thanks fletch-j

- If sin(x)=4/5 for x E [0,pi/2] and tan(y)=5/12 for y E [pi,3pi/2], find:
-tan(x) answer=4/3
-sec(x) answer=5/3
-sin(x+y) answer=-63/65
-tan(x+2y) answer=-836/123

- If tan(x)=2 and x E [0,pi/2], use trigonometric identities to find the exact values for:
-sin(2x)  answer=4/5
-cos(2x)  answer=-3/5

- Simplify the expression tan(x/2)/(1-tan^2(x/2))