Holiday homeworkk

[TrueTears]

-1-i is in the 3rd quadrant, so it is clearly not . You're better off doing this by sketching and using trigonometry. The arctan formula is not true in all quadrants.

This is so true, don't just remember the formula's, sketch and play around, derive the formula's yourself

[TrueTears]

Also take a look at : http://vcenotes.com/forum/index.php/topic,16487.msg171347.html#msg171347

XD

[mandy]

Also take a look at : http://vcenotes.com/forum/index.php/topic,16487.msg171347.html#msg171347

XD

Omg, I'm such an idiot, lol. Thank you kamil and TrueTears, I'll actually remember it this time - cos I've made the same mistake in the same question twice.

[mandy]

For with , find the value of x (do not evaluate ).

I can do it if I evaluate , but they specifically told me not to, so what do I do :S

[kamil9876]

The red line has length . However so does the other red line since it's length is . They both have hypotenuse equal to (the green) and both have a right angle in between the blue and red line. Hence they are the same traingle only flipped over. Now the angle between green and red line is . Therefore

In fact you should do these kinds of things in general, as there are some nice identities relating and . You should try derive them.


edit: angle between green and red is

[mandy]

Thank you Kamil, I think I get it .. But now I've got a question where variables are concerned.

For with where , find in terms of .

This is what I have:
From the question:
And from an identity:

I tried to do some equating and some transposing, but that was useless and I got as the answer. The correct answer is meant to be .

What am I meant to be doing here?

[brightsky]

I suggest you not do it by identities but following your train of thought...

  [1]

     [2]

Substitute [2] into [1]:

[brightsky]

How do you derive this identity? I'm veryy lost when it comes to the unit circle! ><

[kamil9876]

you can use my diagram again. This time is the length of the red line. hence using the same reasoning as in the previous post(which i edited after realising a small mistake now):

 


The identites themselves can be derived from this sort or argument. I suggest understanding the argument more since the formulas aren't very useful for manipulating algebraically and the argument is easier to remember and be flexible with for a variety of questions. Though knowing that the identities exist is useful so that you know where you're supposed to go, though the actual argument/justification should be in the geometry.

[kamil9876]

How do you derive this identity? I'm veryy lost when it comes to the unit circle! ><

Prove that the angle between the two green lines is 90degrees. This gives the identity when is in first quadrant. Now apply this argument for other quadrants.

Alternatively you can use compound angle formula but that is cheating.

[brightsky]

Oh I see. Thanks!!

[mandy]

I'm having trouble with this question:

For with where , find a in terms of b.

Can someone give me a clue or tell me where to start?

[kamil9876]

Period of tan function.

[mandy]

Okay, I still don't know what to do. So the is in the 3rd quadrant and the is in the 1st quadrant. And in both these quadrants, is positive. What do I do now?

[cipherpol]

Is the answer something like ?