Trigonometry Examples

Solve for C (9.9)^2=(8.4)^2+(8.7)^2-2*8.4*8.7cos(C)
Step 1
Rewrite the equation as .
Step 2
Simplify .
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Step 2.1
Simplify each term.
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Step 2.1.1
Raise to the power of .
Step 2.1.2
Raise to the power of .
Step 2.1.3
Multiply by .
Step 2.1.4
Multiply by .
Step 2.2
Add and .
Step 3
Raise to the power of .
Step 4
Move all terms not containing to the right side of the equation.
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Step 4.1
Subtract from both sides of the equation.
Step 4.2
Subtract from .
Step 5
Divide each term in by and simplify.
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Step 5.1
Divide each term in by .
Step 5.2
Simplify the left side.
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Step 5.2.1
Cancel the common factor of .
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Step 5.2.1.1
Cancel the common factor.
Step 5.2.1.2
Divide by .
Step 5.3
Simplify the right side.
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Step 5.3.1
Divide by .
Step 6
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Step 7
Simplify the right side.
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Step 7.1
Evaluate .
Step 8
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 9
Simplify .
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Step 9.1
Multiply by .
Step 9.2
Subtract from .
Step 10
Find the period of .
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Step 10.1
The period of the function can be calculated using .
Step 10.2
Replace with in the formula for period.
Step 10.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 10.4
Divide by .
Step 11
The period of the function is so values will repeat every radians in both directions.
, for any integer