Trigonometry Examples

Find the Cosine Given the Point (4,-2 square root of 3)
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
Simplify the expression.
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Step 2.1.1
Raise to the power of .
Step 2.1.2
Apply the product rule to .
Step 2.1.3
Raise to the power of .
Step 2.2
Rewrite as .
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Step 2.2.1
Use to rewrite as .
Step 2.2.2
Apply the power rule and multiply exponents, .
Step 2.2.3
Combine and .
Step 2.2.4
Cancel the common factor of .
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Step 2.2.4.1
Cancel the common factor.
Step 2.2.4.2
Rewrite the expression.
Step 2.2.5
Evaluate the exponent.
Step 2.3
Simplify the expression.
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Step 2.3.1
Multiply by .
Step 2.3.2
Add and .
Step 2.4
Rewrite as .
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Step 2.4.1
Factor out of .
Step 2.4.2
Rewrite as .
Step 2.5
Pull terms out from under the radical.
Step 3
therefore .
Step 4
Simplify .
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Step 4.1
Cancel the common factor of and .
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Step 4.1.1
Factor out of .
Step 4.1.2
Cancel the common factors.
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Step 4.1.2.1
Factor out of .
Step 4.1.2.2
Cancel the common factor.
Step 4.1.2.3
Rewrite the expression.
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.