cos(arcsin(x))

Simplify cos(arcsin(x))
👋 Follow @integralsforyou on Instagram for a daily integral 😉
📸 @integralsforyou / integralsforyou
𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝𝐬 𝐩𝐥𝐚𝐲𝐥𝐢𝐬𝐭
► Integration by parts
• 🧑‍🔧 Integration by parts
► Integration by substitution
• 🧑‍🔧 Integration by sub...
► Integration by trig substitution
• 🧑‍🔧 Integration by tri...
► Integration by Weierstrass substitution
• 🧑‍🔧 Integration by Wei...
► Integration by partial fraction decomposition
• 🧑‍🔧 Integration by par...
𝐅𝐨𝐥𝐥𝐨𝐰 𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬 𝐅𝐨𝐫𝐘𝐨𝐮
▶️ RUclips: www.youtube.co...
📸 Instagram: / integralsforyou
👍 Facebook: / integralsforyou
𝐃𝐨𝐧𝐚𝐭𝐞
🙋‍♂️ Patreon: / integralsforyou
#integralsforyou #integrals #integration

[@IntegralsForYou]

👋 Follow @integralsforyou for a daily integral 😉
📸 instagram.com/integralsforyou/
𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝𝐬 𝐩𝐥𝐚𝐲𝐥𝐢𝐬𝐭
► Integration by parts
ruclips.net/p/PLpfQkODxXi4-GdH-W7YvTuKmK_mFNxW_h
► Integration by substitution
ruclips.net/p/PLpfQkODxXi4-7Nc5OlXc0zs81dgwnQQc4
► Integration by trig substitution
ruclips.net/p/PLpfQkODxXi49OUGvTetsTW61kUs6wHnzT
► Integration by Weierstrass substitution
ruclips.net/p/PLpfQkODxXi4-8kbKt63rs1xwo6e3yAage
► Integration by partial fraction decomposition
ruclips.net/p/PLpfQkODxXi4-9Ts0IMGxzI5ssWNBT9aXJ
𝐅𝐨𝐥𝐥𝐨𝐰 𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬 𝐅𝐨𝐫𝐘𝐨𝐮
▶️ RUclips
ruclips.net/user/integralsforyou
📸 Instagram
instagram.com/integralsforyou/
👍 Facebook
facebook.com/IntegralsForYou
𝐃𝐨𝐧𝐚𝐭𝐞
🙋‍♂️ Patreon
www.patreon.com/integralsforyou

[@taikb1900]

I'm sorry but b/a=x/1 does not imply b=x and a=1.
Nevertheless, having b/a=x is enough to conclude.
Indeed, as a^2-b^2=c^2 => 1-(b/a)^2=1-x^2=(c/a)^2 ( a not equal to 0)
and thus cos(arcsin(x))=c/a=√1-x^2

[@IntegralsForYou]

Thank you! 😊

[@IzayoiMeiHigu]

you are being a big help for me !!
thank you so much !
I wish the best for you !!

[@IntegralsForYou]

Thank you Izayoi, I'm very happy to know it :-D

[@afaloky3502]

thank you, this method is very useful because i don't understand how my teacher do

[@IntegralsForYou]

😊😊

[@BeBassist]

Several mistakes:
1) Theta could be negative. You have to argue why you can suppose it to be non-negative.
2) Come on, b/a = x/1 does not always imply that b = x and a = 1 !!!!!!!!!!!!!!!!!!! You only can write that b = a.x ... Or you say that you can assume w.l.o.g. that you're working in a right-angled triangle with a = 1 and then obviously b = x.

[@simodahbi5890]

You completely all right I mean look it this b\a= x\1 gives b=x a=1 that's crazy !!!!!!

[@almirak2164]

Bien vu ! Mais ce qu'il a écrit est juste (vrai) UNIQUEMENT dans un cercle trigonométrique de rayon r=1 (r=hyp). Mais si r > 1, tout deviendra faux
صحيح ما كتبه عندما يكون نصف قطر الدائرة يساوي واحد

[@SteamPunkLV]

Thanks a bunch!! This pretty much explains how you can derive all the identities for trigonometric functions of inverse trigonometric functions :)

[@IntegralsForYou]

;-D Another way to do it can be:
1 = sin^2(theta) + cos^2(theta)
Let theta = arcsin(x) then:
1 = sin^2(arcsin(x)) + cos^2(arcsin(x))
1 = x^2 + cos^2(arcsin(x))
1 - x^2 = cos^2(arcsin(x))
sqrt(1 - x^2) = cos(arcsin(x))

[@piero4200]

@@IntegralsForYou before I saw this video , I tried this method. When you do the root, don't you have to take the positive and negative values? I stopped because I dind't know wich ones to take.
Sorry if I wrote something but I am italian.

[@IntegralsForYou]

@@piero4200 Ciao, Piero! Prima di tutto, il tuo inglese si capisce come il mio italiano :). Secondo, puoi trovare la risposta a la tua domanda qua => math.stackexchange.com/questions/1118400/trig-substitution-why-can-we-ignore-the-absolute-value

[@piero4200]

@@IntegralsForYou thank you very much

[@IntegralsForYou]

@@piero4200 You're welcome!

[@user-cu4if6nz2j]

非常感谢您的分享！解决了我的疑惑！

[@IntegralsForYou]

You're welcome! ;-D

[@brettshore964]

Dear god you just saved me from a calculus induced hernia. Thank you

[@IntegralsForYou]

😂😍😎

[@anthonyver1288]

rly, good stuff

[@IntegralsForYou]

Thanks! 💪

[@skskskisisis]

Thank you ❣️❣️❣️

[@IntegralsForYou]

My pleasure! 💪💪

[@dangerouslevi5204]

so nice thanks for help

[@IntegralsForYou]

You're welcome! 😊

[@varvara3199]

Thank you, this is amazing. Helped so much❤️

[@IntegralsForYou]

Thanks, Varvara! 😉

[@lpslolinha]

thank you so much! It was so easy after all!!

[@IntegralsForYou]

;-D

[@erikabonilla8157]

thankyousomuch!!

[@IntegralsForYou]

You're welcome! 😊

[@esraozer1465]

Thank you 🇹🇷🤗

[@IntegralsForYou]

You're welcome, Esra! ;-D

[@bilalerenyavuz1826]

Thanks man great video!

[@IntegralsForYou]

Thanks! 💪

[@tevinnavinda768]

Thanks

[@IntegralsForYou]

My pleasure! ☺

[@joebagot4122]

beautifully proved

[@IntegralsForYou]

Thanks! 😊

[@jackstolar3218]

great help. I wish I found you sooner

[@IntegralsForYou]

Thanks, Jack Stolar! ;-D

[@weebql676]

thanks bro, i had that watch videos of other lenguague for learn xD, regards from chile!!

[@IntegralsForYou]

Gracias nicoisaac! Si tienes alguna duda siempre puedes preguntarme en el idioma que te apetezca ;-D

[@juniorpena4873]

Español y audio

[@meiyiwang9187]

[@IntegralsForYou]

Thanks! 💪

[@carlosbryanperedamontes8845]

Thank u

[@IntegralsForYou]

😊

[@imaneainaki8588]

what???
if we have 3/4 = 6/8 that means that 3=6 and 4 =8 ???

[@ichweisskeiname]

no, but you can fix any value, here a =1 (like the radius of the unit circle), and then the other value is determined

[@user-fz2rd1wc7c]

R

[@user-ot4ly8eq4s]

THx.....just

[@IntegralsForYou]

;-D

[@fedaykln]

adam adam

[@melihhopa2684]

[@IntegralsForYou]

❤️😎

[@jerrari7323]

وذندن

[@burakd8229]

i can only see a hand