Trigonometry Examples

Solve for ? cos(x-1)^2=0
Step 1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 2
Simplify .
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Step 2.1
Rewrite as .
Step 2.2
Pull terms out from under the radical, assuming positive real numbers.
Step 2.3
Plus or minus is .
Step 3
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Step 4
Simplify the right side.
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Step 4.1
The exact value of is .
Step 5
Add to both sides of the equation.
Step 6
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 7
Solve for .
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Step 7.1
Simplify .
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Step 7.1.1
To write as a fraction with a common denominator, multiply by .
Step 7.1.2
Combine fractions.
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Step 7.1.2.1
Combine and .
Step 7.1.2.2
Combine the numerators over the common denominator.
Step 7.1.3
Simplify the numerator.
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Step 7.1.3.1
Multiply by .
Step 7.1.3.2
Subtract from .
Step 7.2
Add to both sides of the equation.
Step 8
Find the period of .
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Step 8.1
The period of the function can be calculated using .
Step 8.2
Replace with in the formula for period.
Step 8.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 8.4
Divide by .
Step 9
The period of the function is so values will repeat every radians in both directions.
, for any integer
Step 10
Consolidate the answers.
, for any integer