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Trigonometry Examples
Step 1
Step 1.1
Simplify .
Step 1.1.1
Expand using the FOIL Method.
Step 1.1.1.1
Apply the distributive property.
Step 1.1.1.2
Apply the distributive property.
Step 1.1.1.3
Apply the distributive property.
Step 1.1.2
Simplify and combine like terms.
Step 1.1.2.1
Simplify each term.
Step 1.1.2.1.1
Multiply by .
Step 1.1.2.1.2
Move to the left of .
Step 1.1.2.1.3
Multiply by .
Step 1.1.2.2
Add and .
Step 1.2
Subtract from both sides of the inequality.
Step 1.3
Convert the inequality to an equation.
Step 1.4
Use the quadratic formula to find the solutions.
Step 1.5
Substitute the values , , and into the quadratic formula and solve for .
Step 1.6
Simplify.
Step 1.6.1
Simplify the numerator.
Step 1.6.1.1
Raise to the power of .
Step 1.6.1.2
Multiply by .
Step 1.6.1.3
Apply the distributive property.
Step 1.6.1.4
Multiply by .
Step 1.6.1.5
Multiply by .
Step 1.6.1.6
Add and .
Step 1.6.2
Multiply by .
Step 1.7
Simplify the expression to solve for the portion of the .
Step 1.7.1
Simplify the numerator.
Step 1.7.1.1
Raise to the power of .
Step 1.7.1.2
Multiply by .
Step 1.7.1.3
Apply the distributive property.
Step 1.7.1.4
Multiply by .
Step 1.7.1.5
Multiply by .
Step 1.7.1.6
Add and .
Step 1.7.2
Multiply by .
Step 1.7.3
Change the to .
Step 1.8
Simplify the expression to solve for the portion of the .
Step 1.8.1
Simplify the numerator.
Step 1.8.1.1
Raise to the power of .
Step 1.8.1.2
Multiply by .
Step 1.8.1.3
Apply the distributive property.
Step 1.8.1.4
Multiply by .
Step 1.8.1.5
Multiply by .
Step 1.8.1.6
Add and .
Step 1.8.2
Multiply by .
Step 1.8.3
Change the to .
Step 1.9
Consolidate the solutions.
Step 2
Step 2.1
Rewrite in slope-intercept form.
Step 2.1.1
The slope-intercept form is , where is the slope and is the y-intercept.
Step 2.1.2
Remove parentheses.
Step 2.1.3
Simplify .
Step 2.1.3.1
Split the fraction into two fractions.
Step 2.1.3.2
Split the fraction into two fractions.
Step 2.1.3.3
Move the negative in front of the fraction.
Step 2.1.4
Arrange the polynomial to follow the form for slope and y-intercept.
Step 2.1.5
Combine .
Step 2.1.5.1
Combine the numerators over the common denominator.
Step 2.1.5.2
Simplify the expression.
Step 2.1.5.2.1
Add and .
Step 2.1.5.2.2
Divide by .
Step 2.1.6
Rewrite in slope-intercept form.
Step 2.2
Since the equation is a vertical line, it does not cross the y-axis.
No y-intercept
Step 2.3
Since the equation is a vertical line, the slope is infinite.
Step 3