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Precalculus Examples
Step 1
Step 1.1
To find the x-intercept(s), substitute in for and solve for .
Step 1.2
Solve the equation.
Step 1.2.1
Rewrite the equation as .
Step 1.2.2
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Step 1.2.3
Simplify the right side.
Step 1.2.3.1
The exact value of is .
Step 1.2.4
The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth quadrant.
Step 1.2.5
Simplify .
Step 1.2.5.1
To write as a fraction with a common denominator, multiply by .
Step 1.2.5.2
Combine fractions.
Step 1.2.5.2.1
Combine and .
Step 1.2.5.2.2
Combine the numerators over the common denominator.
Step 1.2.5.3
Simplify the numerator.
Step 1.2.5.3.1
Multiply by .
Step 1.2.5.3.2
Subtract from .
Step 1.2.6
Find the period of .
Step 1.2.6.1
The period of the function can be calculated using .
Step 1.2.6.2
Replace with in the formula for period.
Step 1.2.6.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 1.2.6.4
Divide by .
Step 1.2.7
The period of the function is so values will repeat every radians in both directions.
, for any integer
Step 1.2.8
Consolidate the answers.
, for any integer
, for any integer
Step 1.3
x-intercept(s) in point form.
x-intercept(s): , for any integer
x-intercept(s): , for any integer
Step 2
Step 2.1
To find the y-intercept(s), substitute in for and solve for .
Step 2.2
Solve the equation.
Step 2.2.1
Remove parentheses.
Step 2.2.2
The exact value of is .
Step 2.3
y-intercept(s) in point form.
y-intercept(s):
y-intercept(s):
Step 3
List the intersections.
x-intercept(s): , for any integer
y-intercept(s):
Step 4