Trigonometry Examples

Find the Cosecant Given the Point ((2 square root of 2)/3,1/3)
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
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
Simplify the expression.
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Step 2.3.1
Raise to the power of .
Step 2.3.2
Multiply by .
Step 2.3.3
Apply the product rule to .
Step 2.3.4
One to any power is one.
Step 2.3.5
Raise to the power of .
Step 2.3.6
Combine the numerators over the common denominator.
Step 2.3.7
Add and .
Step 2.3.8
Divide by .
Step 2.3.9
Any root of is .
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
Multiply by .