VCE Methods Question Thread!

[keltingmeith]

find all solutions to |cos(2x)|=1/2 ?!?!
how does the mod affect this question

Try solving this graphically as opposed to algebraically, see if you notice anything.

[lzxnl]

It means cos(2x) = +-1/2

Or, if you want, cos^2 (2x) = 1/4
Double angle formula gives (1 + cos 4x)/2 = 1/4 (optional)
cos 4x = -1/2

[I_I]

Hello,
just a question I encountered during solving the problem

((-pi/2 +1)²)^1/2

I always thought this was (-pi/2 +1) as the powers cancel each other out, but it's not?

The answer is (pi-2)/2.... why is this?

Thanks in advance!
Catherine

[keltingmeith]

Hello,
just a question I encountered during solving the problem

((-pi/2 +1)²)^1/2

I always thought this was (-pi/2 +1) as the powers cancel each other out, but it's not?

The answer is (pi-2)/2.... why is this?

Thanks in advance!
Catherine

The powers don't cancel out, as the ranges of the square root function and quadratic function are non-negative, and 1-pi/2 is negative.

[Ha_Nguyen]

It means cos(2x) = +-1/2

Or, if you want, cos^2 (2x) = 1/4
Double angle formula gives (1 + cos 4x)/2 = 1/4 (optional)
cos 4x = -1/2

hi, i think i've worked it out... do i find cos(pi/3) in all quadrants because since it is mod, everything becomes positive..
so that means the answer is:
pi/3, 2pi/3, 4pi/3, 5pi/3, and all of these with 2(pi)n added to them?? what does it mean when it says to find "all" solutions? do i put the 2(pi)n?
Thanks

[keltingmeith]

Hey guys, just getting stuck on this question
Solve

Any help or pointers would be appreciated. Thanks!

Use your calculator.

[lzxnl]

Hey guys, just getting stuck on this question
Solve

Any help or pointers would be appreciated. Thanks!

x=-1

I'm not kidding. I just looked at that and that was my instinct. If they're going to give you something like this without a calculator, the numbers are going to be nice.

[Ha_Nguyen]

Hey guys, really stuck on these

for each of the following statements either prove it is true or give a counterexample

a) for all real numbers x, sin-1(sinx)=x
b) for all x belonging to [-1,1], sin(sin-1(x))=x

thanks

[cooldude123]

Use your calculator.

It was a tech-free question (sorry forgot to mention)

x=-1

So trial and error is the best method for these sorts of problems?

[keltingmeith]

Hey guys, really stuck on these

for each of the following statements either prove it is true or give a counterexample

a) for all real numbers x, sin-1(sinx)=x
b) for all x belonging to [-1,1], sin(sin-1(x))=x

thanks

First one is false - let x=3pi/2:



Second one is true, proving it is easy based on the definition of the inverse.

It was a tech-free question (sorry forgot to mention)

Well, it's a bad question and it should feel bad. :|

[kinslayer]

It was a tech-free question (sorry forgot to mention)

So trial and error is the best method for these sorts of problems?

In a sense, it's the only method. Generally speaking, there's no exact solution to that type of equation, so if you're asked to give one without a calculator, it is going to be easy.

The term is your clue that the answer is -1 since it makes the exponent zero.

[RazzMeTazz]

Can a set contain more than one of the same element?

For e.g. A= {1,2,3,4} and B = {1,6,7}

Does this mean that A U B = {1,1,2,3,4,6,7}

? Thanks

[wunderkind52]

Can a set contain more than one of the same element?

For e.g. A= {1,2,3,4} and B = {1,6,7}

Does this mean that A U B = {1,1,2,3,4,6,7}

? Thanks

i think you CAN have a set that contain duplicate elements, but they don't really count as "different" so {1,1,3} is the same as {1,3}. So in your answer AUB, you wouldn't include the duplicate elements

[kinslayer]

Can a set contain more than one of the same element?

For e.g. A= {1,2,3,4} and B = {1,6,7}

Does this mean that A U B = {1,1,2,3,4,6,7}

? Thanks

Sets are collections of distinct elements. In your example

[RazzMeTazz]

Thanks for the great explanations wunderkind52 and kinslayer