Prove Inverse Trigonometric Functions

Joined
Jun 27, 2021
Messages
5,386
Reaction score
422
I am having a hard time understanding what needs to be done with proving inverse trigonometric functions. For example, what is she doing in this video lesson?

 
prove: cos(sin^-1(x))=sqrt(1-x^2)

let sin^-1(x)=y

then cos(sin^-1(x))=cos(y) where -pi/2<= y<= pi/2 , then cos(y) >=0

use identity cos^2(y)+sin^2(y)=1..........solve for cos

cos^2(y)=1-sin^2(y)
cos(y)=sqrt(1-sin^2(y))......since sin^-1(x)=y, we can write that sin(y)=x =>sin^2(y)=x^2

substitute sin^2(y)=x^2 and sin^-1(x)=y in cos(y)=sqrt(1-sin^2(y)) and we have:

cos(sin^-1(x))=sqrt(1-x^2)

 
prove: cos(sin^-1(x))=sqrt(1-x^2)

let sin^-1(x)=y

then cos(sin^-1(x))=cos(y) where -pi/2<= y<= pi/2 , then cos(y) >=0

use identity cos^2(y)+sin^2(y)=1..........solve for cos

cos^2(y)=1-sin^2(y)
cos(y)=sqrt(1-sin^2(y))......since sin^-1(x)=y, we can write that sin(y)=x =>sin^2(y)=x^2

substitute sin^2(y)=x^2 and sin^-1(x)=y in cos(y)=sqrt(1-sin^2(y)) and we have:

cos(sin^-1(x))=sqrt(1-x^2)

Your reply is better than Ms. Shaws' but still not clear enough for me to try on my own. Enough! Moving on.
 


Write your reply...

Members online

No members online now.

Forum statistics

Threads
2,529
Messages
9,858
Members
696
Latest member
fairdistribution
Back
Top