Trigonometry Examples

Solve for θ in Degrees 2cos(theta)-3=5cos(theta)-5
Step 1
Move all terms containing to the left side of the equation.
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Step 1.1
Subtract from both sides of the equation.
Step 1.2
Subtract from .
Step 2
Move all terms not containing to the right side of the equation.
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Step 2.1
Add to both sides of the equation.
Step 2.2
Add and .
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
Dividing two negative values results in a positive value.
Step 4
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Step 5
Simplify the right side.
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Step 5.1
Evaluate .
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
Subtract from .
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 degrees in both directions.
, for any integer