Trigonometry Examples

Find the Cosine Given the Point (1/( square root of 5),-2/( square root of 5))
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
Multiply by .
Step 2.2
Combine and simplify the denominator.
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Step 2.2.1
Multiply by .
Step 2.2.2
Raise to the power of .
Step 2.2.3
Raise to the power of .
Step 2.2.4
Use the power rule to combine exponents.
Step 2.2.5
Add and .
Step 2.2.6
Rewrite as .
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Step 2.2.6.1
Use to rewrite as .
Step 2.2.6.2
Apply the power rule and multiply exponents, .
Step 2.2.6.3
Combine and .
Step 2.2.6.4
Cancel the common factor of .
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Step 2.2.6.4.1
Cancel the common factor.
Step 2.2.6.4.2
Rewrite the expression.
Step 2.2.6.5
Evaluate the exponent.
Step 2.3
Apply the product rule to .
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
Raise to the power of .
Step 2.6
Cancel the common factor of and .
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Step 2.6.1
Factor out of .
Step 2.6.2
Cancel the common factors.
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Step 2.6.2.1
Factor out of .
Step 2.6.2.2
Cancel the common factor.
Step 2.6.2.3
Rewrite the expression.
Step 2.7
Multiply by .
Step 2.8
Combine and simplify the denominator.
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Step 2.8.1
Multiply by .
Step 2.8.2
Raise to the power of .
Step 2.8.3
Raise to the power of .
Step 2.8.4
Use the power rule to combine exponents.
Step 2.8.5
Add and .
Step 2.8.6
Rewrite as .
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Step 2.8.6.1
Use to rewrite as .
Step 2.8.6.2
Apply the power rule and multiply exponents, .
Step 2.8.6.3
Combine and .
Step 2.8.6.4
Cancel the common factor of .
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Step 2.8.6.4.1
Cancel the common factor.
Step 2.8.6.4.2
Rewrite the expression.
Step 2.8.6.5
Evaluate the exponent.
Step 2.9
Use the power rule to distribute the exponent.
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Step 2.9.1
Apply the product rule to .
Step 2.9.2
Apply the product rule to .
Step 2.9.3
Apply the product rule to .
Step 2.10
Simplify the expression.
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Step 2.10.1
Raise to the power of .
Step 2.10.2
Multiply by .
Step 2.11
Simplify the numerator.
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Step 2.11.1
Raise to the power of .
Step 2.11.2
Rewrite as .
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Step 2.11.2.1
Use to rewrite as .
Step 2.11.2.2
Apply the power rule and multiply exponents, .
Step 2.11.2.3
Combine and .
Step 2.11.2.4
Cancel the common factor of .
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Step 2.11.2.4.1
Cancel the common factor.
Step 2.11.2.4.2
Rewrite the expression.
Step 2.11.2.5
Evaluate the exponent.
Step 2.12
Reduce the expression by cancelling the common factors.
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Step 2.12.1
Raise to the power of .
Step 2.12.2
Multiply by .
Step 2.12.3
Cancel the common factor of and .
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Step 2.12.3.1
Factor out of .
Step 2.12.3.2
Cancel the common factors.
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Step 2.12.3.2.1
Factor out of .
Step 2.12.3.2.2
Cancel the common factor.
Step 2.12.3.2.3
Rewrite the expression.
Step 2.12.4
Simplify the expression.
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Step 2.12.4.1
Combine the numerators over the common denominator.
Step 2.12.4.2
Add and .
Step 2.12.4.3
Divide by .
Step 2.12.4.4
Any root of is .
Step 3
therefore .
Step 4
Simplify .
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Step 4.1
Divide by .
Step 4.2
Multiply by .
Step 4.3
Combine and simplify the denominator.
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Step 4.3.1
Multiply by .
Step 4.3.2
Raise to the power of .
Step 4.3.3
Raise to the power of .
Step 4.3.4
Use the power rule to combine exponents.
Step 4.3.5
Add and .
Step 4.3.6
Rewrite as .
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Step 4.3.6.1
Use to rewrite as .
Step 4.3.6.2
Apply the power rule and multiply exponents, .
Step 4.3.6.3
Combine and .
Step 4.3.6.4
Cancel the common factor of .
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Step 4.3.6.4.1
Cancel the common factor.
Step 4.3.6.4.2
Rewrite the expression.
Step 4.3.6.5
Evaluate the exponent.
Step 5
Approximate the result.