This turned out to be harder than I originally thought it would. The problem is that the x-axis is showing ticks for t
, not the plotting variable x
, so it is important that the relation between t
and x
be clearly shown. Further, the OP requested that the information about the relationship be displayed as an x-axis label. That condition caused trouble. I found I couldn't use the option PlotLabels
to label the two curves because Mathematica insisted on overwriting the x-axis label with the cosine curve label. I had to resort to using callouts with some explicit positioning.
Plot[
{Callout[Sin[x], Sin[x]], Callout[Cos[x], Cos[x], {5 π/2 + 1.2, .6}]},
{x, 0, 5 π/2},
LabelStyle -> {Bold, 12},
AxesLabel -> {Row[{t, ", ", HoldForm[x = π/2], "\[ThinSpace]", t}], "C"},
Ticks -> {{# π/2, #} & /@ Range[1, 5, 2], Automatic},
ImagePadding -> All,
ImageSize -> 500]

The above conforms to my understanding of what the OP is asking for, but for myself I wouldn't make the plot that way. I would make it like this:
Plot[
{Callout[Sin[π t/2 ], Sin[π t/2 ]], Callout[Cos[π t/2], Cos[π t/2], {5 + .9, .4}]},
{t, 0, 5},
LabelStyle -> {Bold, 11},
AxesLabel -> {"t", "C"},
ImagePadding -> All,
ImageSize -> 500]

I believe the second plot gets the point across better with simpler code. That's two pluses.
Update
I was really unhappy that I had not been able to post a solution using PlotLabels
and Placed
, so I returned to this problem, spent some time reading the documentation more carefully and trying this and that. After going down some wrong paths, I finally found a way.
Plot[{Sin[x], Cos[x]}, {x, 0, 5 π/2},
LabelStyle -> {Bold, 12},
AxesLabel -> {Row[{t, ", ", HoldForm[x = π/2], "\[ThinSpace]", t}], "C"},
Ticks -> {{# π/2, #} & /@ Range[1, 5, 2], Automatic},
PlotLabels ->
Placed["Expressions", {{Scaled[.2], Above}, {Scaled[.82], Above}}],
ImageSize -> 500]

The trick is to give the 2nd argument to Placed
, the position specifier, as a list of two elements, one for each curve. Each element should be a pair of the form {offset, position}
, where offset is a scaled distance along the x-axis and position indicates where the label should be positioned relative to curve at the offset (the usual Above
, Before
, etc.). This is never explicitly stated in the documentation, but there is an example of a list plot that hints at this solution.
Ticks -> {{{Pi/2, Style["π/2"]}, {3 Pi/2, Style["3π/2"]}, {5 Pi/2, Style["5π/2"]}}}
) to give this. $\endgroup$