# Find the X and Y Intercepts y=cos(1/2x)

To find the x-intercept, substitute in for and solve for .
Solve the equation.
Rewrite the equation as .
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
The exact value of is .
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
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.
Multiply both sides of the equation by .
Simplify both sides of the equation.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
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 .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Subtract from .
The resulting angle of is positive, less than , 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.
is approximately which is positive so remove the absolute value
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
The period of the function is so values will repeat every radians in both directions.
, for any integer
, for any integer
To find the y-intercept, substitute in for and solve for .
Simplify .
Multiply by .
The exact value of is .
These are the and intercepts of the equation .
x-intercept: , for any integer
y-intercept:
Find the X and Y Intercepts y=cos(1/2x)