Trigonometry Examples

Find the Cosecant Given the Point (1/2,-( square root of 3)/2)
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
Apply the product rule to .
Step 2.2
One to any power is one.
Step 2.3
Raise to the power of .
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 2.5
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
Rewrite as .
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Step 2.6.1
Use to rewrite as .
Step 2.6.2
Apply the power rule and multiply exponents, .
Step 2.6.3
Combine and .
Step 2.6.4
Cancel the common factor of .
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Step 2.6.4.1
Cancel the common factor.
Step 2.6.4.2
Rewrite the expression.
Step 2.6.5
Evaluate the exponent.
Step 2.7
Simplify the expression.
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Step 2.7.1
Raise to the power of .
Step 2.7.2
Combine the numerators over the common denominator.
Step 2.7.3
Add and .
Step 2.7.4
Divide by .
Step 2.7.5
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
Raise to the power of .
Step 4.5.3
Raise to the power of .
Step 4.5.4
Use the power rule to combine exponents.
Step 4.5.5
Add and .
Step 4.5.6
Rewrite as .
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Step 4.5.6.1
Use to rewrite as .
Step 4.5.6.2
Apply the power rule and multiply exponents, .
Step 4.5.6.3
Combine and .
Step 4.5.6.4
Cancel the common factor of .
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Step 4.5.6.4.1
Cancel the common factor.
Step 4.5.6.4.2
Rewrite the expression.
Step 4.5.6.5
Evaluate the exponent.
Step 5
Approximate the result.