# How do you find the domain of #g(x) = (3^(x+1)) / (sin x + cos x) #?

##### 1 Answer

#### Explanation:

For this problem, we have to ask ourselves a couple of questions.

•When does

#sinx + cosx# equal#0# .

•What is the domain of#3^(x + 1)#

I'll start by answering the first one. Solve the trigonometric equation.

#sinx + cosx = 0#

Square both sides

#(sinx + cosx)^2 = 0^2#

#sin^2x + 2sinxcosx + cos^2x = 0#

Apply

#1 + 2sinxcosx = 0#

Use

#1 + sin2x = 0#

#sin2x = -1#

#2x = arcsin(-1)#

#2x = (3pi)/2 + 2pin# because the sine function has a period of#2pi#

#x = (3pi)/4 + pin#

This means that whenever

Let's answer the second question.

This means that the domain of

Hopefully this helps!