# Precalculus Examples

Solve for ? sin(x)=cos(x)
Step 1
Divide each term in the equation by .
Step 2
Convert from to .
Step 3
Cancel the common factor of .
Step 3.1
Cancel the common factor.
Step 3.2
Rewrite the expression.
Step 4
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Step 5
Simplify the right side.
Step 5.1
The exact value of is .
Step 6
The tangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from to find the solution in the fourth quadrant.
Step 7
Simplify .
Step 7.1
To write as a fraction with a common denominator, multiply by .
Step 7.2
Combine fractions.
Step 7.2.1
Combine and .
Step 7.2.2
Combine the numerators over the common denominator.
Step 7.3
Simplify the numerator.
Step 7.3.1
Move to the left of .
Step 7.3.2
Step 8
Find the period of .
Step 8.1
The period of the function can be calculated using .
Step 8.2
Replace with in the formula for period.
Step 8.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 8.4
Divide by .
Step 9
The period of the function is so values will repeat every radians in both directions.
, for any integer
Step 10