Trigonometry Examples

Find the Sine Given the Point (-( square root of 2)/5,( square root of 23)/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
Use the power rule to distribute the exponent.
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Step 2.1.1
Apply the product rule to .
Step 2.1.2
Apply the product rule to .
Step 2.2
Simplify the expression.
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Step 2.2.1
Raise to the power of .
Step 2.2.2
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
Raise to the power of .
Step 2.4.2
Apply the product rule to .
Step 2.5
Rewrite as .
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Step 2.5.1
Use to rewrite as .
Step 2.5.2
Apply the power rule and multiply exponents, .
Step 2.5.3
Combine and .
Step 2.5.4
Cancel the common factor of .
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Step 2.5.4.1
Cancel the common factor.
Step 2.5.4.2
Rewrite the expression.
Step 2.5.5
Evaluate the exponent.
Step 2.6
Simplify the expression.
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Step 2.6.1
Raise to the power of .
Step 2.6.2
Combine the numerators over the common denominator.
Step 2.6.3
Add and .
Step 2.6.4
Divide by .
Step 2.6.5
Any root of is .
Step 3
therefore .
Step 4
Divide by .
Step 5
Approximate the result.