# Trigonometry Examples

Convert to Interval Notation square root of 2sin(x)+ square root of 2cos(x)>0
Divide each term in the equation by .
Factor out of .
Replace with an equivalent expression in the numerator.
Remove parentheses.
Apply the distributive property.
Rewrite in terms of sines and cosines.
Apply the distributive property.
Multiply .
Combine and .
Combine and .
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Simplify each term.
Separate fractions.
Convert from to .
Divide by .
Separate fractions.
Convert from to .
Divide by .
Multiply by .
Subtract from both sides of the inequality.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
The exact value of is .
The tangent function is negative in the second and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the third quadrant.
Simplify the expression to find the second solution.
Simplify .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Move the negative in front of the fraction.
The resulting angle of is positive and coterminal with .
Find the period.
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
Add to every negative angle to get positive angles.
Add to to find the positive angle.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Move to the left of .
Subtract from .
List the new angles.
The period of the function is so values will repeat every radians in both directions.
, for any integer
Convert the inequality to interval notation.