Trigonometry Examples

Find the Cosecant Given the Point (6,-8)
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
Raise to the power of .
Step 2.2
Raise to the power of .
Step 2.3
Add and .
Step 2.4
Rewrite as .
Step 2.5
Pull terms out from under the radical, assuming positive real numbers.
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
Move the negative in front of the fraction.
Step 5
Approximate the result.