Question

Which are properties of both y=arcsin x and y=x/(sq.rt 1-x^2) ?

a. y(0)=0

b. Increasing everywhere

c. Concave down for x < 0

d. Domain: [-1, 1]

e. Range: (-∞, ∞)

**not sure how to determine which one it is!! :/ please explain? :) thank you!!

Answer 1

oh and the whole thing is under the sq.rt. for the 1-x^2 part...

draw still isn't working! :/

Answer 2

Easiest way is to graph both.

https://www.google.com/search?q=arccsc(x)&oq=arccsc(x)&aqs=chrome..69i57j0l5.4243j0j4&sourceid=chrome&espv=210&es_sm=93&ie=UTF-8#q=arcsin(x)%2C+x%2Fsqrt(1-x%5E2)&safe=off

Answer 3

Domain of the second is clearly not [-1, 1] since you can't plug -1 or 1 in, w/o a denominator of 0.

Both are increasing.

Range isn't the same.

Both concave down for x<0

both are 0 when x=0

Answer 4

ohh okay, so it would be increasing everywhere, concaving down at x<0 and y(0)=0 ?

not sure if that last one is right?

would it be a,b, and c are true?

Answer 5

Looks right. Last is clearly not true, arcsin's range is [-1, 1]

Answer 6

ahh okay i see :) awesome! thank you!!!