Trigonometry Examples

Find the Cosecant Given the Point ((2 square root of 13)/13,-(3 square root of 13)/13)
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 numerator.
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Step 2.2.1
Raise to the power of .
Step 2.2.2
Rewrite as .
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Step 2.2.2.1
Use to rewrite as .
Step 2.2.2.2
Apply the power rule and multiply exponents, .
Step 2.2.2.3
Combine and .
Step 2.2.2.4
Cancel the common factor of .
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Step 2.2.2.4.1
Cancel the common factor.
Step 2.2.2.4.2
Rewrite the expression.
Step 2.2.2.5
Evaluate the exponent.
Step 2.3
Reduce the expression by cancelling the common factors.
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Step 2.3.1
Raise to the power of .
Step 2.3.2
Multiply by .
Step 2.3.3
Cancel the common factor of and .
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Step 2.3.3.1
Factor out of .
Step 2.3.3.2
Cancel the common factors.
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Step 2.3.3.2.1
Factor out of .
Step 2.3.3.2.2
Cancel the common factor.
Step 2.3.3.2.3
Rewrite the expression.
Step 2.4
Use the power rule to distribute the exponent.
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Step 2.4.1
Apply the product rule to .
Step 2.4.2
Apply the product rule to .
Step 2.4.3
Apply the product rule to .
Step 2.5
Simplify the expression.
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Step 2.5.1
Raise to the power of .
Step 2.5.2
Multiply by .
Step 2.6
Simplify the numerator.
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Step 2.6.1
Raise to the power of .
Step 2.6.2
Rewrite as .
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Step 2.6.2.1
Use to rewrite as .
Step 2.6.2.2
Apply the power rule and multiply exponents, .
Step 2.6.2.3
Combine and .
Step 2.6.2.4
Cancel the common factor of .
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Step 2.6.2.4.1
Cancel the common factor.
Step 2.6.2.4.2
Rewrite the expression.
Step 2.6.2.5
Evaluate the exponent.
Step 2.7
Reduce the expression by cancelling the common factors.
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Step 2.7.1
Raise to the power of .
Step 2.7.2
Multiply by .
Step 2.7.3
Cancel the common factor of and .
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Step 2.7.3.1
Factor out of .
Step 2.7.3.2
Cancel the common factors.
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Step 2.7.3.2.1
Factor out of .
Step 2.7.3.2.2
Cancel the common factor.
Step 2.7.3.2.3
Rewrite the expression.
Step 2.7.4
Simplify the expression.
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Step 2.7.4.1
Combine the numerators over the common denominator.
Step 2.7.4.2
Add and .
Step 2.7.4.3
Divide by .
Step 2.7.4.4
Any root of is .
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
Rewrite as .
Step 4.1.2
Move the negative in front of the fraction.
Step 4.2
Multiply the numerator by the reciprocal of the denominator.
Step 4.3
Multiply by .
Step 4.4
Multiply by .
Step 4.5
Combine and simplify the denominator.
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Step 4.5.1
Multiply by .
Step 4.5.2
Move .
Step 4.5.3
Raise to the power of .
Step 4.5.4
Raise to the power of .
Step 4.5.5
Use the power rule to combine exponents.
Step 4.5.6
Add and .
Step 4.5.7
Rewrite as .
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Step 4.5.7.1
Use to rewrite as .
Step 4.5.7.2
Apply the power rule and multiply exponents, .
Step 4.5.7.3
Combine and .
Step 4.5.7.4
Cancel the common factor of .
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Step 4.5.7.4.1
Cancel the common factor.
Step 4.5.7.4.2
Rewrite the expression.
Step 4.5.7.5
Evaluate the exponent.
Step 4.6
Cancel the common factor of .
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Step 4.6.1
Cancel the common factor.
Step 4.6.2
Rewrite the expression.
Step 5
Approximate the result.