Video Transcript
Find the value of the cos of 11๐
over six.
We begin by noticing that our angle
is given in radians, and we recall that ๐ radians is equal to 180 degrees. Dividing both values by six, we see
that ๐ over six radians is equal to 30 degrees. We can then multiply both sides of
this equation by 11, showing us that 11๐ over six radians is equal to 330
degrees. This means that the value we need
to calculate is the cos of 330 degrees. We can do this by firstly sketching
the graph of the cosine function and then using our knowledge of special angles.
The cosine function is periodic and
has a maximum value of one and a minimum value of negative one. The graph of ๐ฆ equals cos of ๐
between zero and 360 degrees is shown. We want to calculate the cos of 330
degrees. From our graph, we can see that
this is positive and lies between zero and one. Due to the symmetry of the cosine
function, we can see from our graph that the cos of 330 degrees is equal to the cos
of 30 degrees. One of the special angles we need
to recall is that the cos of 30 degrees is equal to root three over two. This means that the cos of 330
degrees is also equal to root three over two. The cos of 11๐ over six radians
is, therefore, also equal to root three over two.
