Question

Find the implied domain and range of y=cos(2arcsinx)

can someone please check if im solving it correctly? Thanks

Answer 1

u=2arcsinx -------> Range of arcsinx [-pi/2,pi/2]

cos has restricted the domain: [0,pi]

Answer 2

in the textbook it has the domain [0,1] and range [-1,1]. is it correct?

Answer 3

can someone please correct me if im wrong but my answer is: domain [0,sqrt2/2] and range [0,1]

Answer 4

@loser66

Answer 5

2arcsin x has domain [-1,1] and range [-pi,pi ]
from cos , we need cos (-pi) = -1 and cos (pi) = -1 also.
However, among [-pi,pi] we have the value of pi/2 which gives us cos (pi/2) = 0
so that the range of cos is [-1,0]

Answer 6

https://www.desmos.com/calculator/2djmpyhbrf

Answer 7

Isn't the range from cos supposed to be [-1,1]

Answer 8

oh, yes, you are right. I am sorry.