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

  1. Recall the sine value of 60 degrees

    The sine of 60 degrees is known and can be found in trigonometric tables or memorized:

    $$ \sin(60^{\circ}) = \frac{\sqrt{3}}{2} $$

  2. Find the reciprocal of sine to get cosecant

    The cosecant function is the reciprocal of the sine function:

    $$ \csc(60^{\circ}) = \frac{1}{\sin(60^{\circ})} $$

  3. Substitute the value of sine

    Substitute the known value of $ \sin(60^{\circ}) $ into the reciprocal function:

    $$ \csc(60^{\circ}) = \frac{1}{\frac{\sqrt{3}}{2}} $$

  4. 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.

Thank you for voting!
Use Quizgecko on...
Browser
Browser