Trigonometry Examples

Find the Sine Given the Point (-1/4,-3/4)
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
Raise to the power of .
Step 2.3
Multiply by .
Step 2.4
One to any power is one.
Step 2.5
Raise to the power of .
Step 2.6
Use the power rule to distribute the exponent.
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Step 2.6.1
Apply the product rule to .
Step 2.6.2
Apply the product rule to .
Step 2.7
Simplify the expression.
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Step 2.7.1
Raise to the power of .
Step 2.7.2
Multiply by .
Step 2.7.3
Raise to the power of .
Step 2.7.4
Raise to the power of .
Step 2.7.5
Combine the numerators over the common denominator.
Step 2.7.6
Add and .
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
Rewrite as .
Step 2.10
Simplify the denominator.
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Step 2.10.1
Rewrite as .
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Step 2.10.1.1
Factor out of .
Step 2.10.1.2
Rewrite as .
Step 2.10.2
Pull terms out from under the radical.
Step 2.11
Multiply by .
Step 2.12
Combine and simplify the denominator.
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Step 2.12.1
Multiply by .
Step 2.12.2
Move .
Step 2.12.3
Raise to the power of .
Step 2.12.4
Raise to the power of .
Step 2.12.5
Use the power rule to combine exponents.
Step 2.12.6
Add and .
Step 2.12.7
Rewrite as .
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Step 2.12.7.1
Use to rewrite as .
Step 2.12.7.2
Apply the power rule and multiply exponents, .
Step 2.12.7.3
Combine and .
Step 2.12.7.4
Cancel the common factor of .
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Step 2.12.7.4.1
Cancel the common factor.
Step 2.12.7.4.2
Rewrite the expression.
Step 2.12.7.5
Evaluate the exponent.
Step 2.13
Simplify the numerator.
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Step 2.13.1
Combine using the product rule for radicals.
Step 2.13.2
Multiply by .
Step 2.14
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
Move the leading negative in into the numerator.
Step 4.2.2
Cancel the common factor.
Step 4.2.3
Rewrite the expression.
Step 4.3
Combine and .
Step 4.4
Move the negative in front of the fraction.
Step 4.5
Multiply by .
Step 4.6
Combine and simplify the denominator.
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Step 4.6.1
Multiply by .
Step 4.6.2
Raise to the power of .
Step 4.6.3
Raise to the power of .
Step 4.6.4
Use the power rule to combine exponents.
Step 4.6.5
Add and .
Step 4.6.6
Rewrite as .
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Step 4.6.6.1
Use to rewrite as .
Step 4.6.6.2
Apply the power rule and multiply exponents, .
Step 4.6.6.3
Combine and .
Step 4.6.6.4
Cancel the common factor of .
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Step 4.6.6.4.1
Cancel the common factor.
Step 4.6.6.4.2
Rewrite the expression.
Step 4.6.6.5
Evaluate the exponent.
Step 5
Approximate the result.