Trigonometry Examples

Find the Tangent Given the Point (( square root of 5)/4,(- square root of 11)/4)
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
Multiply the numerator by the reciprocal of the denominator.
Step 3.2
Cancel the common factor of .
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Step 3.2.1
Cancel the common factor.
Step 3.2.2
Rewrite the expression.
Step 3.3
Combine and .
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
Raise to the power of .
Step 3.5.3
Raise to the power of .
Step 3.5.4
Use the power rule to combine exponents.
Step 3.5.5
Add and .
Step 3.5.6
Rewrite as .
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Step 3.5.6.1
Use to rewrite as .
Step 3.5.6.2
Apply the power rule and multiply exponents, .
Step 3.5.6.3
Combine and .
Step 3.5.6.4
Cancel the common factor of .
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Step 3.5.6.4.1
Cancel the common factor.
Step 3.5.6.4.2
Rewrite the expression.
Step 3.5.6.5
Evaluate the exponent.
Step 3.6
Simplify the numerator.
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Step 3.6.1
Combine using the product rule for radicals.
Step 3.6.2
Multiply by .
Step 4
Approximate the result.