Trigonometry Examples

Find the Cotangent Given the Point (3 1/2,-2 square root of 15)
Step 1
To find the between the x-axis and the line between the points and , draw the triangle between the three points , , and .
Opposite :
Adjacent :
Step 2
therefore .
Step 3
Simplify .
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Step 3.1
Convert to an improper fraction.
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Step 3.1.1
A mixed number is an addition of its whole and fractional parts.
Step 3.1.2
Add and .
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Step 3.1.2.1
To write as a fraction with a common denominator, multiply by .
Step 3.1.2.2
Combine and .
Step 3.1.2.3
Combine the numerators over the common denominator.
Step 3.1.2.4
Simplify the numerator.
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Step 3.1.2.4.1
Multiply by .
Step 3.1.2.4.2
Add and .
Step 3.2
Multiply the numerator by the reciprocal of the denominator.
Step 3.3
Move the negative in front of the fraction.
Step 3.4
Multiply by .
Step 3.5
Combine and simplify the denominator.
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Step 3.5.1
Multiply by .
Step 3.5.2
Move .
Step 3.5.3
Raise to the power of .
Step 3.5.4
Raise to the power of .
Step 3.5.5
Use the power rule to combine exponents.
Step 3.5.6
Add and .
Step 3.5.7
Rewrite as .
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Step 3.5.7.1
Use to rewrite as .
Step 3.5.7.2
Apply the power rule and multiply exponents, .
Step 3.5.7.3
Combine and .
Step 3.5.7.4
Cancel the common factor of .
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Step 3.5.7.4.1
Cancel the common factor.
Step 3.5.7.4.2
Rewrite the expression.
Step 3.5.7.5
Evaluate the exponent.
Step 3.6
Multiply by .
Step 3.7
Multiply .
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Step 3.7.1
Multiply by .
Step 3.7.2
Multiply by .
Step 4
Approximate the result.