Trigonometry Examples

Find the Cosecant Given the Point (-2, square root of 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
Raise to the power of .
Step 2.2
Rewrite as .
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Step 2.2.1
Use to rewrite as .
Step 2.2.2
Apply the power rule and multiply exponents, .
Step 2.2.3
Combine and .
Step 2.2.4
Cancel the common factor of .
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Step 2.2.4.1
Cancel the common factor.
Step 2.2.4.2
Rewrite the expression.
Step 2.2.5
Evaluate the exponent.
Step 2.3
Add and .
Step 3
therefore .
Step 4
Simplify .
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Step 4.1
Multiply by .
Step 4.2
Combine and simplify the denominator.
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Step 4.2.1
Multiply by .
Step 4.2.2
Raise to the power of .
Step 4.2.3
Raise to the power of .
Step 4.2.4
Use the power rule to combine exponents.
Step 4.2.5
Add and .
Step 4.2.6
Rewrite as .
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Step 4.2.6.1
Use to rewrite as .
Step 4.2.6.2
Apply the power rule and multiply exponents, .
Step 4.2.6.3
Combine and .
Step 4.2.6.4
Cancel the common factor of .
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Step 4.2.6.4.1
Cancel the common factor.
Step 4.2.6.4.2
Rewrite the expression.
Step 4.2.6.5
Evaluate the exponent.
Step 4.3
Simplify the numerator.
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Step 4.3.1
Combine using the product rule for radicals.
Step 4.3.2
Multiply by .
Step 5
Approximate the result.