# Find the X and Y Intercepts f(x)=4cos(2x-pi) To find the x-intercept, substitute in for and solve for .
Solve the equation.
Rewrite the equation as .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
The exact value of is .
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.
Simplify the right side of the equation.
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 .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Multiply .
Multiply and .
Multiply by .
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.
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 all terms not containing to the right side of the equation.
Add to both sides of the equation.
Simplify the right side of the equation.
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 .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Multiply .
Multiply and .
Multiply by .
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 .
Cancel the common factor of .
Cancel the common factor.
Divide by .
The period of the function is so values will repeat every radians in both directions.
, for any integer
, for any integer
, for any integer
To find the y-intercept, substitute in for and solve for .
Simplify .
Multiply by .
Subtract from .
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.
The exact value of is .
Multiply by .
Multiply by .
These are the and intercepts of the equation .
x-intercept: , for any integer
y-intercept:
Find the X and Y Intercepts f(x)=4cos(2x-pi)     