Trigonometry Examples

Find the Roots (Zeros) cos(3theta)=1
Step 1
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Step 2
Simplify the right side.
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Step 2.1
The exact value of is .
Step 3
Divide each term in by and simplify.
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Step 3.1
Divide each term in by .
Step 3.2
Simplify the left side.
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Step 3.2.1
Cancel the common factor of .
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Step 3.2.1.1
Cancel the common factor.
Step 3.2.1.2
Divide by .
Step 3.3
Simplify the right side.
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Step 3.3.1
Divide by .
Step 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 5
Solve for .
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Step 5.1
Simplify.
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Step 5.1.1
Multiply by .
Step 5.1.2
Add and .
Step 5.2
Divide each term in by and simplify.
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Step 5.2.1
Divide each term in by .
Step 5.2.2
Simplify the left side.
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Step 5.2.2.1
Cancel the common factor of .
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Step 5.2.2.1.1
Cancel the common factor.
Step 5.2.2.1.2
Divide by .
Step 6
Find the period of .
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Step 6.1
The period of the function can be calculated using .
Step 6.2
Replace with in the formula for period.
Step 6.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 7
The period of the function is so values will repeat every radians in both directions.
, for any integer
Step 8
Consolidate the answers.
, for any integer
Step 9