You've thoroughly convinced me that math can be fun. I used to hate math... Trig Identities is by far the funnest thing I've played with in math so far.
Thanks for showing how identities are derived. I strongly suggest relating these concepts to the unit circle for anyone struggling with ideas like cos(-x) = cos(x). So much easier when you know the signs of the trig functions in the different quadrants of the coordinate plane.
It's because of Pythagorean's theorem: x^2 + y^2 = c^2 where 'x' is the length on the x-axis, 'y' is the length on the y-axis, and 'c' is the hypotenuse. None of these values can ever be negative.
i love u khan.... i always hated to remember things that i don get.. like trig identities in precalc... now that they make sense its not only fun, i can also memorize them easily.... this is gonna help me so much when i take calc ... THANK YOU KHAN!!!!! UR THE MAN!!!!!!!!
When did the sin or cos ever become specific to the x or y axis? As I understand it the sin and cos exist with respect to a given angle (sin=o/h, cos=a/h). so the opposite and adjacent sides would only be defined with respect to the angle used. So using a different angle on the same right triangle could flip whether the sin or cos is on the on the x and y axis respectively. Between 4:05 and 4:25, you specifically state that cos is defined as 0 and sin as 1? Are their other videos that explain this point?
+Jassen Yep yes. I have watched those videos before, and did so again after your comment in case missed or forgot something. I see your point; however, unless I'm missing something, sin can only be y in cases where theta has a coordinate of the triangle in the closest proximity to the center of the unit circle . If theta is the angle that is farthest away from the center of the unit circle, then sin flips to the x axis, because the "oppesite" would become the x axis and the "adjacent" the y axis. This being the case, it questions the universal use of the y axis being universally applied to sin. Does that make sense?
love videos:-)should switched x&y to respective axis' before@2:40 make ez In unit circle, don't need soh cah toa all hypotenuse = 1, (stuff÷1 = stuff) sin of angle wants "y of angle" (y/1) yaxis cos of angle wants "x of angle" (x/1) xaxis sin θ = y cos θ = x tan θ = y/x = sin/cos stuff = stuff/1 inverse by flip "if flip" stuff/1 "then get" 1/stuff csc θ = 1/y (sin flip) sec θ = 1/x (cos flip) cotan θ = x/y (tan flip) = cos/sin
wait wouldn't cos(-a) be equal to -cos(a)? because although the hypotenuse remains the same( hypotenuse is never negative) the adjacent side become negative.
Because for compound angle formulae you want to be able to use a and b instead of like θ and... um... μ I guess? Or λ? It's just a convenience thing. θ is often used to represent unknown angles, only when there's just one angle.
Cosine rules over the x (horizontal) axis which goes from negative to positive in the right direction. Since he was dealing with quadrants I and IV of the unit circle, x was only positive, so the values cannot be negative. Thus, cos(-b)=cos(b). As the other guy said it.
the entire semester i have not been able to understand how this makes sense until now. you have saved me b4 finals. ty
You've thoroughly convinced me that math can be fun. I used to hate math... Trig Identities is by far the funnest thing I've played with in math so far.
Back when youtube had a 10 min limit lol
Why is it when I watch KhanAcademy, I suddenly understand everything, but when my teacher teaches this, I get so confused. LOL
I Need MORE MAAAAATH!!!!!!!!
thank you for taking the time out your day to help everybody else.
keep up the good work
Thanks for showing how identities are derived. I strongly suggest relating these concepts to the unit circle for anyone struggling with ideas like cos(-x) = cos(x). So much easier when you know the signs of the trig functions in the different quadrants of the coordinate plane.
It's because of Pythagorean's theorem: x^2 + y^2 = c^2 where 'x' is the length on the x-axis, 'y' is the length on the y-axis, and 'c' is the hypotenuse. None of these values can ever be negative.
i love u khan.... i always hated to remember things that i don get.. like trig identities in precalc... now that they make sense its not only fun, i can also memorize them easily.... this is gonna help me so much when i take calc ... THANK YOU KHAN!!!!! UR THE MAN!!!!!!!!
IM FASCINATED!!!!!! THIS IS MAGIC
thanks man you helped me do my college trig homework without even ever having to go to class!!!
My exact question was sin(a-b) and you got half way through the equation and left me hanging, man!
as pufalupagus said, the hypothenuse can't be negative. Try to use the Unit Circle and figure it out :)
Fascinating!!!
your the reason i got into university
nice video and thumbs up!
Thank you sir. I can truely understand every of your video. You helped me alot :D
You my friend, have magnificent explanation skills!
Thank you!
Thank you sir
good explanation you are the best
this stuff is amazing
This is great.
When did the sin or cos ever become specific to the x or y axis? As I understand it the sin and cos exist with respect to a given angle (sin=o/h, cos=a/h). so the opposite and adjacent sides would only be defined with respect to the angle used. So using a different angle on the same right triangle could flip whether the sin or cos is on the on the x and y axis respectively. Between 4:05 and 4:25, you specifically state that cos is defined as 0 and sin as 1? Are their other videos that explain this point?
Chris Bouwhuis go watch the unit circle video- that will explain a lot
+Jassen Yep yes. I have watched those videos before, and did so again after your comment in case missed or forgot something. I see your point; however, unless I'm missing something, sin can only be y in cases where theta has a coordinate of the triangle in the closest proximity to the center of the unit circle . If theta is the angle that is farthest away from the center of the unit circle, then sin flips to the x axis, because the "oppesite" would become the x axis and the "adjacent" the y axis. This being the case, it questions the universal use of the y axis being universally applied to sin. Does that make sense?
Yes, so if hypotenuse = 1
then, soh cah toa = so÷1 ca÷1 toa
stuff÷1 = stuff/1 = stuff
love videos:-)should switched x&y to respective axis' before@2:40 make ez
In unit circle, don't need soh cah toa
all hypotenuse = 1, (stuff÷1 = stuff)
sin of angle wants "y of angle" (y/1) yaxis
cos of angle wants "x of angle" (x/1) xaxis
sin θ = y
cos θ = x
tan θ = y/x = sin/cos
stuff = stuff/1
inverse by flip
"if flip" stuff/1 "then get" 1/stuff
csc θ = 1/y (sin flip)
sec θ = 1/x (cos flip)
cotan θ = x/y (tan flip) = cos/sin
Guys, I believe this is a mistake : at 1:56 I think he meant to write sin (-a) = -1 X sin x/h (as he says earlier, just before writing)
hypotenuse is never negative.
How is cos Pi/2= 0, and sin pi/2=1, is it not the opposite?
this video was made 5 days after my birthday
You've misspelled "identities" in the title. Great video, by the way! :D
@TheDRASC14 NO! the adjacent side is the same for both a AND -a... think about it :D
wait wouldn't cos(-a) be equal to -cos(a)? because although the hypotenuse remains the same( hypotenuse is never negative) the adjacent side become negative.
I cannot believe im doing this stuff at 15 years old. Seriously!
Well when should you be doing it? Everyone does this stuff at 15...
I was hoping to find a proof for reducing powers of trig functions.
you tube had a 10 min limit
That cough really shocked me out -________-
why is op -op but h not -h in the other triangle??
@oppertunityknocks No sir! I got dis! :)
4:39, scared the hell out of me. Headphones
Why the switch from ø to A?
Because for compound angle formulae you want to be able to use a and b instead of like θ and... um... μ I guess? Or λ? It's just a convenience thing. θ is often used to represent unknown angles, only when there's just one angle.
Where the hell is part 4
why cos-b =cos b
can anyone explain it
The answer is in the first part of this video when he flips a triangle and compares it to the radius circle.
Cosine rules over the x (horizontal) axis which goes from negative to positive in the right direction. Since he was dealing with quadrants I and IV of the unit circle, x was only positive, so the values cannot be negative. Thus, cos(-b)=cos(b).
As the other guy said it.
The magnitude of the angle doesn't change, why would the cosine of the angle be any different?
love you, i love you so much im going to cut my arm and wirte you a poem with my blood !!! ^^