Thread: domain

the function f(x)=ln(sinx) is defined for all x in which of the following intervals?
a) 0<x<pi
b)0<= x <= pi
c) 3pi/2<x<5pi/2
d)3pi/2 <= x <= 5pi/2
e) 3pi/2<x< 2pi

Originally Posted by sandiego234

the function f(x)=ln(sinx) is defined for all x in which of the following intervals?
a) 0<x<pi
b)0<= x <= pi
c) 3pi/2<x<5pi/2
d)3pi/2 <= x <= 5pi/2
e) 3pi/2<x< 2pi

I will give you a big hint ...so find the interval on which and you have yoru partial domain

is it A?

please verify. thank you.

0 would give sin0=0
sin pi= 0
sinpi/3= root3/2
sinpi/2 = 1

Originally Posted by sandiego234

the function f(x)=ln(sinx) is defined for all x in which of the following intervals?
a) 0<x<pi
b)0<= x <= pi
c) 3pi/2<x<5pi/2
d)3pi/2 <= x <= 5pi/2
e) 3pi/2<x< 2pi

Think, AND , but to get positive values of sine, then it must be in the 1st and 2nd quadrants, or

are you sure this is right?

if it were to be 0<= x<= pi
then sin pi is zero, meaning ln(0)= undefined....
also sin(0)= 0, meaning ln(0)
that would not be part of the domain therefore.