### Video Transcript

For the given function π of π‘
equals two csc two π‘ π plus three tan π‘ π, evaluate π of π by four.

Here, π is a vector-valued
function. Itβs a function whose range is a
set of vectors. And we can evaluate π of π by
four in much the usual way by substituting π‘ equals π by four into each component
function. For the horizontal component, the
component of π, we get two csc two times π by four. Of course, we know that csc π₯ is
equal to one over sin π₯ and two times π by four is equal to π over two. So this becomes two over sin of π
by two. And since sin π by two is simply
one, we end up with two divided by one, which is two. We repeat this for the vertical
component for π. Thatβs three tan of π by four. And of course, tan of π by four is
simply one. So thatβs three times one, which is
three. That means that π of π by four is
two π plus three π. Contextually, this gives us the
position of a point in the plane when π‘ is equal to π by four.