Trigonometry Examples

Solve for B cos(B)=(5^2+8^2-8^2)/(2*5*8)
Step 1
Simplify .
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Step 1.1
Simplify the numerator.
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Step 1.1.1
Raise to the power of .
Step 1.1.2
Raise to the power of .
Step 1.1.3
Raise to the power of .
Step 1.1.4
Multiply by .
Step 1.1.5
Add and .
Step 1.1.6
Subtract from .
Step 1.2
Simplify the denominator.
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Step 1.2.1
Multiply by .
Step 1.2.2
Multiply by .
Step 1.3
Cancel the common factor of and .
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Step 1.3.1
Factor out of .
Step 1.3.2
Cancel the common factors.
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Step 1.3.2.1
Factor out of .
Step 1.3.2.2
Cancel the common factor.
Step 1.3.2.3
Rewrite the expression.
Step 2
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Step 3
Simplify the right side.
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Step 3.1
Evaluate .
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
Simplify .
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Step 5.1
Multiply by .
Step 5.2
Subtract from .
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 6.4
Divide by .
Step 7
The period of the function is so values will repeat every radians in both directions.
, for any integer