csc of 60 degrees
Understand the Problem
The question is asking for the cosecant of 60 degrees, which is a trigonometric function. We will need to recall the value of sine for 60 degrees and then take the reciprocal to find cosecant.
Answer
$ \frac{2\sqrt{3}}{3} $
Answer for screen readers
The final answer is $ \frac{2\sqrt{3}}{3} $
Steps to Solve
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Recall the sine value of 60 degrees
The sine of 60 degrees is known and can be found in trigonometric tables or memorized:
$$ \sin(60^{\circ}) = \frac{\sqrt{3}}{2} $$
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Find the reciprocal of sine to get cosecant
The cosecant function is the reciprocal of the sine function:
$$ \csc(60^{\circ}) = \frac{1}{\sin(60^{\circ})} $$
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Substitute the value of sine
Substitute the known value of $ \sin(60^{\circ}) $ into the reciprocal function:
$$ \csc(60^{\circ}) = \frac{1}{\frac{\sqrt{3}}{2}} $$
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Simplify the reciprocal
To simplify, multiply the numerator and denominator by 2:
$$ \csc(60^{\circ}) = \frac{2}{\sqrt{3}} $$
For exact values, rationalize the denominator:
$$ \csc(60^{\circ}) = \frac{2\sqrt{3}}{3} $$
The final answer is $ \frac{2\sqrt{3}}{3} $
More Information
In trigonometry, the 'cosecant' is the reciprocal of the 'sine' function. It's vital to know the fundamental trigonometric values to quickly find cosecant values.
Tips
A common mistake is to forget to rationalize the denominator. This step helps in keeping the final answer in a standard mathematical form.
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