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Trigonometry Examples
Step 1
Step 1.1
Set the argument of the logarithm equal to zero.
Step 1.2
Solve for .
Step 1.2.1
Take the inverse arctangent of both sides of the equation to extract from inside the arctangent.
Step 1.2.2
Simplify the right side.
Step 1.2.2.1
The exact value of is .
Step 1.2.3
Divide each term in by and simplify.
Step 1.2.3.1
Divide each term in by .
Step 1.2.3.2
Simplify the left side.
Step 1.2.3.2.1
Cancel the common factor of .
Step 1.2.3.2.1.1
Cancel the common factor.
Step 1.2.3.2.1.2
Divide by .
Step 1.2.3.3
Simplify the right side.
Step 1.2.3.3.1
Divide by .
Step 1.2.4
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 1.2.5
Simplify .
Step 1.2.5.1
Rewrite as .
Step 1.2.5.2
Pull terms out from under the radical, assuming positive real numbers.
Step 1.2.5.3
Plus or minus is .
Step 1.3
The vertical asymptote occurs at .
Vertical Asymptote:
Vertical Asymptote:
Step 2
Step 2.1
Replace the variable with in the expression.
Step 2.2
Simplify the result.
Step 2.2.1
One to any power is one.
Step 2.2.2
Multiply by .
Step 2.2.3
Evaluate .
Step 2.2.4
The final answer is .
Step 3
Step 3.1
Replace the variable with in the expression.
Step 3.2
Simplify the result.
Step 3.2.1
Raise to the power of .
Step 3.2.2
Multiply by .
Step 3.2.3
Evaluate .
Step 3.2.4
The final answer is .
Step 4
Step 4.1
Replace the variable with in the expression.
Step 4.2
Simplify the result.
Step 4.2.1
Raise to the power of .
Step 4.2.2
Multiply by .
Step 4.2.3
Evaluate .
Step 4.2.4
The final answer is .
Step 5
The log function can be graphed using the vertical asymptote at and the points .
Vertical Asymptote:
Step 6