#### To determine

**To Sketch**

the graph of the function y=ln(sinx)

#### Answer

The Sketch of the curve y=ln(sinx) is given below

#### Explanation

**Steps in Curve tracing**

**A. Domain:** Given y=ln(sinx)

Since it is defined for all values of sinx>0

Therefore, the domain is {x|x>0}

**B. Intercepts:** No y Intercept

x intercept is obtained by taking y=0

Therefore,ln(sinx)=0⇒sinx=1⇒x=π2

**C. Symmetry:**

The curve is not symmetrical about bothaxes.

**D. Asymptotes:**

There are no horizontal asymptotes and vertical asymptotes

**E. Interval of increase and decrease**

y=ln(sinx)y′=tanx

The function is increasing when tanx is positive and decreasing when tanx is negative

**F. Local maxima and minima**

Maxima and minima are obtained by the first derivative test,

i.e., y′=tanx=0⇒x=0

Since for x=0, the function is not defined, no local maxima or minima

**G. Concavity and inflexion points**

y′=tanxy″=sec2xy″=0⇒sec2x=0

No inflexion point as sec x is never zero

**H.** Using this information we sketch the curve

**Final statement:**

The sketch of the curve y=ln(sinx) is given below: