Trigonometry Examples

Find the Domain y=sec(2x+pi/4)
Step 1
Set the argument in equal to to find where the expression is undefined.
, for any integer
Step 2
Solve for .
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Step 2.1
Move all terms not containing to the right side of the equation.
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Step 2.1.1
Subtract from both sides of the equation.
Step 2.1.2
To write as a fraction with a common denominator, multiply by .
Step 2.1.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 2.1.3.1
Multiply by .
Step 2.1.3.2
Multiply by .
Step 2.1.4
Combine the numerators over the common denominator.
Step 2.1.5
Subtract from .
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Step 2.1.5.1
Reorder and .
Step 2.1.5.2
Subtract from .
Step 2.2
Divide each term in by and simplify.
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Step 2.2.1
Divide each term in by .
Step 2.2.2
Simplify the left side.
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Step 2.2.2.1
Cancel the common factor of .
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Step 2.2.2.1.1
Cancel the common factor.
Step 2.2.2.1.2
Divide by .
Step 2.2.3
Simplify the right side.
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Step 2.2.3.1
Simplify each term.
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Step 2.2.3.1.1
Multiply the numerator by the reciprocal of the denominator.
Step 2.2.3.1.2
Multiply .
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Step 2.2.3.1.2.1
Multiply by .
Step 2.2.3.1.2.2
Multiply by .
Step 3
The domain is all values of that make the expression defined.
Set-Builder Notation:
, for any integer
Step 4