math1001: differential calculus (2 Viewers)
- Thread starter Carlito
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a quick question guys... if you're given like a polar form and was ask to convert it back to cartesian form, alright i know how to do that but what happens when theta isnt an exact value
so for example
4(cos 3Pi/4 + i sin 3Pi/4)
how do i convert the 3Pi/4 into an equivalent value so that i can obtain the exact value?
Thanks guys.
so for example
4(cos 3Pi/4 + i sin 3Pi/4)
how do i convert the 3Pi/4 into an equivalent value so that i can obtain the exact value?
Thanks guys.
Angles of any magnitude.
E.g sinx = sin (180 - x), - sinx = sin (180 + x)
Check your prelim 2 unit books.
So sin 3pi/4 = sin pi/4, because sinx = sin (180 - x) as stated above, and pi - 3pi/4 = pi/4.
PS Xayma, how did you do the Pi and square root symbols?????????///
E.g sinx = sin (180 - x), - sinx = sin (180 + x)
Check your prelim 2 unit books.
So sin 3pi/4 = sin pi/4, because sinx = sin (180 - x) as stated above, and pi - 3pi/4 = pi/4.
PS Xayma, how did you do the Pi and square root symbols?????????///
- sin x = sin (360 - x) or sin x = - sin (360 - x) (simply multiplied both sides by -1)
So sin 5p/3 = - sin p/3.
cos x = cos (360 - x)
So cos 5p/3 = cos p/3
All this is is like saying sin 150 = sin 30 etc. If for some reason this is all new to you, I HEAVILY suggest you look up some 2 unit theory books and study it. If you can't find it, I'll scan some of my past 2 unit notes for you.
So sin 5p/3 = - sin p/3.
cos x = cos (360 - x)
So cos 5p/3 = cos p/3
All this is is like saying sin 150 = sin 30 etc. If for some reason this is all new to you, I HEAVILY suggest you look up some 2 unit theory books and study it. If you can't find it, I'll scan some of my past 2 unit notes for you.
woh so...
my two main formulas would be ...
sin x = - sin (360 - x)
cos x = cos (360 - x)
right?
so i find the equivalent angle from 5Pi/3 which is 300 degrees and just sub it in, that's it?
... one last thing how come previously you had sin(180 - x) as posted above...lol i'm kinda rusty cause i forgot all this, the 3 month break was bad...
You've got 12 formulas altogether. 3 for each quadrant and each of those 3 corresponding to Sin, Cos or Tan.
They're easy to remember because you have the ASTC rule, that is 'All, Sin, Tan, Cos', meaning that all the ratios are positive in the 1st quadrant, Sin is +ive in the second, Tan is +ive in the third and Cos is +ive in the 4th.
So say you had tan 5p/3. The acute angle is obviously 2p - 5p/3 = p/3.. pretty obvious.
Then you know that tan is NOT positive in the 4th quadrant, so we know that:
- tan x = tan (360 - x), and then simply sub in the values.
Another example:
Cos 4p/3.
The acute angle is obviously p/3. (If you're confused about this, the acute angle simply means the angle from the angle your given to the horizontal axes).
Anyway, we know that Cos is NOT positive in the 3rd quadrant (it's +ive in the 4th like said above), so we have the rule:
- cos x = (180 + x)
Sub in.
They're easy to remember because you have the ASTC rule, that is 'All, Sin, Tan, Cos', meaning that all the ratios are positive in the 1st quadrant, Sin is +ive in the second, Tan is +ive in the third and Cos is +ive in the 4th.
So say you had tan 5p/3. The acute angle is obviously 2p - 5p/3 = p/3.. pretty obvious.
Then you know that tan is NOT positive in the 4th quadrant, so we know that:
- tan x = tan (360 - x), and then simply sub in the values.
Another example:
Cos 4p/3.
The acute angle is obviously p/3. (If you're confused about this, the acute angle simply means the angle from the angle your given to the horizontal axes).
Anyway, we know that Cos is NOT positive in the 3rd quadrant (it's +ive in the 4th like said above), so we have the rule:
- cos x = (180 + x)
Sub in.
sin x = sin (360 + x)
cos x = cos (360 + x)
tan x = tan (360 + x)
sin x = sin (180 - x)
- cos x = cos (180 - x)
- tan x = tan (180 - x)
- sin x = sin (180 + x)
- cos x = cos (180 + x)
tan x = tan (180 + x)
- sin x = sin (360 - x)
cos x = cos (360 - x)
- tan x = tan (360 - x)
All you have to do is remember ASTC. No need to memorise all those formulae.
EDIT: No 12 mini formulae in each quadrant. 12 altogether. 3 for each quadrant.
cos x = cos (360 + x)
tan x = tan (360 + x)
sin x = sin (180 - x)
- cos x = cos (180 - x)
- tan x = tan (180 - x)
- sin x = sin (180 + x)
- cos x = cos (180 + x)
tan x = tan (180 + x)
- sin x = sin (360 - x)
cos x = cos (360 - x)
- tan x = tan (360 - x)
All you have to do is remember ASTC. No need to memorise all those formulae.
EDIT: No 12 mini formulae in each quadrant. 12 altogether. 3 for each quadrant.
ahhh ok i think i remember now lol that looks sooo familar...
but how do we know which one should we use... like ok taking back the 5Pi/3 example, which is equivalent to 300 degrees... ok it looks blatant that i use the two formulas in quadrant 4, but how would i determine what to use generally.
but how do we know which one should we use... like ok taking back the 5Pi/3 example, which is equivalent to 300 degrees... ok it looks blatant that i use the two formulas in quadrant 4, but how would i determine what to use generally.