1. ## 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

2. ## Ok

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 $\displaystyle ln(u(x)),u(x)>0$...so find the interval on which $\displaystyle sin(x)>0$ and you have yoru partial domain

3. is it A?

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

4. 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, $\displaystyle -1 \le sin(x) \le 1$ AND $\displaystyle 0 \ge ln(x)$, but to get positive values of sine, then it must be in the 1st and 2nd quadrants, or $\displaystyle 0 \le x \le \pi$

5. 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.