How to find the exact value of cos ( 5 π ) 6 ?

Question

How to find the exact value of                     cos                  (          5          π          )                    6      ?

Centarxwm · Accepted Answer

Well, the odd multiples of the cosine       p    I   is always -1 hence             cos              (        5        π        )              =    -    1   and                              cos                      (            5            π            )                              6        =    -          1      6      Although if you mean             cos              (                              5            π                    6                )            ,it can be found by using identity             cos              (        π        -        x        )              =    -          cos      x      and             cos              (                              5            π                    6                )            =             cos              (        π        -                  π          6                )            =       -          cos              (                  π          6                )            =       -                  3            2

planelmolarvh8 · Accepted Answer

There are two ways to complete the task, but if you remember the unit circle, you can complete them more quickly.
Convert

\frac{5 π}{6}

to angle degrees by using the equation:

r a d \cdot (\frac{180}{π}) = d e g r e e s

\frac{5 π}{6} \cdot \frac{180}{π} = 150^{\circ}

And we can figure out that the reference angle for

150^{\circ}

is

30^{\circ}

.

{\cos 30}^{\circ} = \frac{\sqrt{3}}{2}

Since

150^{\circ}

is in the 2nd quadrant, we know cosine is negative.

{\cos 30}^{\circ} = \cos (\frac{5 π}{6}) = - \frac{\sqrt{3}}{2}

How to find the exact value of cos (5pi)/6?

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