Holiday homeworkk

[TrueTears]

What happens if you plug in there?

[mandy]

Thanks, but now I've got a really complex looking part.
- ?

How do I make that turn into ?

I tried to put it on a common denominator, but it didn't work for me.

[Cataclysmic]

[mandy]

Thank you Cataclysmic !!!

[TrueTears]

Mandy, do you know why we didn't pick the negative value? (Just to make sure you understand everything )

[mandy]

Mandy, do you know why we didn't pick the negative value? (Just to make sure you understand everything )

Yes, I understand why now. Cataclysmic told me what you said about it being in the first quadrant, where the value is positive, right

Using half angle formulae, find the values of , and tan in simplest form.

Now I don't know how to find the sin part. I used , and let x = . Am I on the right track?

[TrueTears]

Using half angle formulae, find the values of , and tan in simplest form.


Now I don't know how to find the sin part. I used , and let x = . Am I on the right track?

Yeap, continue down that track.

[mandy]

For an acute angle x, . Therefore is equal to:

This is what I did:
I found the value of cosx, by drawing a triangle.
I then subbed these values into
                                                       =
                                                       =

The actual correct answer is meant to be . What am I doing wrong?

[cipherpol]

Your values of was wrong.



, so

, so

sub these values in , and should be correct answer.

[mandy]

Thanks a lot!

[mandy]

If is an acute angle and , find , and without evaluating .

I've already found the sin and cos parts, I just don't know how to do the tan bit.
I think I found , but then what do I do?

[dodgedanpei]

How to simplify


and



Thanks in advance.

[NE2000]

@dodgedanpei

first one









second one












In both cases the key was to first factorize and then recognize that you could convert it to simplify. Trig simplifications are generally just based on basic algebraic manipulation combined with knowledge of the forms you can convert.

[ChristineNguyen]

Sorry another question
Give that tan(2x) = 4root3 / 7    where x --> [0, pie/4)
find the exact value of sin(x)


and


if cos(A) = sin(A-B)sin(B) prove that tan(A-B)tan(B) = 1/2

[TrueTears]

Sorry another question
Give that tan(2x) = 4root3 / 7    where x --> [0, pie/4)
find the exact value of sin(x)


and


if cos(A) = sin(A-B)sin(B) prove that tan(A-B)tan(B) = 1/2

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