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
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
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 $\displaystyle 0 \le x \le \pi$
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.