Question 1139293
.


            You do not need to use "a double-angle identity to find the exact value of each expression."


            Every student,  studying trigonometry,  must know and keep in his  (or her)  memory 
            the values of trigonometric functions of the given remarkable  (particular)  angles.


            In the same way as every student must know the multiplication table.




1.    sin(120°) = {{{sqrt(3)/2}}}.


2.    tan(60°) = {{{sqrt(3)}}}.


3.    {{{cos(4pi/3)}}} = {{{-1/2}}}.


4.    {{{sin(5pi/3)}}} = {{{-sqrt(3)/2}}}.



See these sources


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://en.wikipedia.org/wiki/Trigonometric_functions>https://en.wikipedia.org/wiki/Trigonometric_functions</A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;https://en.wikipedia.org/wiki/Trigonometric_functions


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://en.wikipedia.org/wiki/Unit_circle>https://en.wikipedia.org/wiki/Unit_circle</A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;https://en.wikipedia.org/wiki/Unit_circle


or learn it from any textbook on Trigonometry.



Happy learning this "multiplication table" of Trigonometry !