Trigonometry Examples

Find the X and Y Intercepts f(x)=cos(x)
To find the x-intercept, substitute in for and solve for .
Solve the equation.
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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 .
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 .
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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 .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
Find the period.
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The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
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The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
The period of the function is so values will repeat every radians in both directions.
, for any integer
Consolidate the answers.
, for any integer
, for any integer
To find the y-intercept, substitute in for and solve for .
The exact value of is .
These are the and intercepts of the equation .
x-intercept: , for any integer
y-intercept:
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