Trigonometry Examples

Find the Cosine Given the Point ( square root of 2,- square root of 7)
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
Rewrite as .
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Step 2.1.1
Use to rewrite as .
Step 2.1.2
Apply the power rule and multiply exponents, .
Step 2.1.3
Combine and .
Step 2.1.4
Cancel the common factor of .
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Step 2.1.4.1
Cancel the common factor.
Step 2.1.4.2
Rewrite the expression.
Step 2.1.5
Evaluate the exponent.
Step 2.2
Simplify the expression.
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Step 2.2.1
Apply the product rule to .
Step 2.2.2
Raise to the power of .
Step 2.2.3
Multiply by .
Step 2.3
Rewrite as .
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Step 2.3.1
Use to rewrite as .
Step 2.3.2
Apply the power rule and multiply exponents, .
Step 2.3.3
Combine and .
Step 2.3.4
Cancel the common factor of .
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Step 2.3.4.1
Cancel the common factor.
Step 2.3.4.2
Rewrite the expression.
Step 2.3.5
Evaluate the exponent.
Step 2.4
Simplify the expression.
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Step 2.4.1
Add and .
Step 2.4.2
Rewrite as .
Step 2.5
Pull terms out from under the radical, assuming positive real numbers.
Step 3
therefore .
Step 4
Approximate the result.