Trigonometry Examples

Find the Cosine Given the Point ((- square root of 2)/5,( square root of 2)/2)
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
Find the hypotenuse using Pythagorean theorem .
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Step 2.1
Move the negative in front of the fraction.
Step 2.2
Use the power rule to distribute the exponent.
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Step 2.2.1
Apply the product rule to .
Step 2.2.2
Apply the product rule to .
Step 2.3
Simplify the expression.
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Step 2.3.1
Raise to the power of .
Step 2.3.2
Multiply by .
Step 2.4
Rewrite as .
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Step 2.4.1
Use to rewrite as .
Step 2.4.2
Apply the power rule and multiply exponents, .
Step 2.4.3
Combine and .
Step 2.4.4
Cancel the common factor of .
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Step 2.4.4.1
Cancel the common factor.
Step 2.4.4.2
Rewrite the expression.
Step 2.4.5
Evaluate the exponent.
Step 2.5
Simplify the expression.
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Step 2.5.1
Raise to the power of .
Step 2.5.2
Apply the product rule to .
Step 2.6
Rewrite as .
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Step 2.6.1
Use to rewrite as .
Step 2.6.2
Apply the power rule and multiply exponents, .
Step 2.6.3
Combine and .
Step 2.6.4
Cancel the common factor of .
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Step 2.6.4.1
Cancel the common factor.
Step 2.6.4.2
Rewrite the expression.
Step 2.6.5
Evaluate the exponent.
Step 2.7
Raise to the power of .
Step 2.8
Cancel the common factor of and .
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Step 2.8.1
Factor out of .
Step 2.8.2
Cancel the common factors.
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Step 2.8.2.1
Factor out of .
Step 2.8.2.2
Cancel the common factor.
Step 2.8.2.3
Rewrite the expression.
Step 2.9
To write as a fraction with a common denominator, multiply by .
Step 2.10
To write as a fraction with a common denominator, multiply by .
Step 2.11
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 2.11.1
Multiply by .
Step 2.11.2
Multiply by .
Step 2.11.3
Multiply by .
Step 2.11.4
Multiply by .
Step 2.12
Combine the numerators over the common denominator.
Step 2.13
Simplify the numerator.
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Step 2.13.1
Multiply by .
Step 2.13.2
Add and .
Step 2.14
Rewrite as .
Step 2.15
Simplify the denominator.
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Step 2.15.1
Rewrite as .
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Step 2.15.1.1
Factor out of .
Step 2.15.1.2
Rewrite as .
Step 2.15.2
Pull terms out from under the radical.
Step 2.16
Multiply by .
Step 2.17
Combine and simplify the denominator.
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Step 2.17.1
Multiply by .
Step 2.17.2
Move .
Step 2.17.3
Raise to the power of .
Step 2.17.4
Raise to the power of .
Step 2.17.5
Use the power rule to combine exponents.
Step 2.17.6
Add and .
Step 2.17.7
Rewrite as .
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Step 2.17.7.1
Use to rewrite as .
Step 2.17.7.2
Apply the power rule and multiply exponents, .
Step 2.17.7.3
Combine and .
Step 2.17.7.4
Cancel the common factor of .
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Step 2.17.7.4.1
Cancel the common factor.
Step 2.17.7.4.2
Rewrite the expression.
Step 2.17.7.5
Evaluate the exponent.
Step 2.18
Simplify the numerator.
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Step 2.18.1
Combine using the product rule for radicals.
Step 2.18.2
Multiply by .
Step 2.19
Multiply by .
Step 3
therefore .
Step 4
Simplify .
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Step 4.1
Multiply the numerator by the reciprocal of the denominator.
Step 4.2
Cancel the common factor of .
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Step 4.2.1
Factor out of .
Step 4.2.2
Cancel the common factor.
Step 4.2.3
Rewrite the expression.
Step 4.3
Combine and .
Step 4.4
Combine and into a single radical.
Step 4.5
Cancel the common factor of and .
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Step 4.5.1
Factor out of .
Step 4.5.2
Cancel the common factors.
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Step 4.5.2.1
Factor out of .
Step 4.5.2.2
Cancel the common factor.
Step 4.5.2.3
Rewrite the expression.
Step 4.6
Rewrite as .
Step 4.7
Any root of is .
Step 4.8
Multiply by .
Step 4.9
Combine and simplify the denominator.
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Step 4.9.1
Multiply by .
Step 4.9.2
Raise to the power of .
Step 4.9.3
Raise to the power of .
Step 4.9.4
Use the power rule to combine exponents.
Step 4.9.5
Add and .
Step 4.9.6
Rewrite as .
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Step 4.9.6.1
Use to rewrite as .
Step 4.9.6.2
Apply the power rule and multiply exponents, .
Step 4.9.6.3
Combine and .
Step 4.9.6.4
Cancel the common factor of .
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Step 4.9.6.4.1
Cancel the common factor.
Step 4.9.6.4.2
Rewrite the expression.
Step 4.9.6.5
Evaluate the exponent.
Step 4.10
Combine and .
Step 5
Approximate the result.