Sine function

sin(A+ B)= sin(A)cos(B)+ cos(A)sin(B).

Set $B= 0.25\pi t$ . Of course, there is no "A" such that sin(A)= .5 and cos(A)= 0.25 because [itex]sin^2(A)+ cos^2(A)= 1\ne 0.5^2+ 0.25^2[/tex] but you can both multiply and divide by [itex]\sqrt{0.5^2+ 0.25^2}= \sqrt{5/16}= \sqrt{5}/4[/tex] to get $\frac{\sqrt{5}}{4}(\frac{4}{\sqrt{5}}cos(25\pi t)+ \frac{4}{\sqrt{5}}sin(25\pi t))$ .

Now one problem is that you have and extra ")" with no corresponding "(". Did you mean $sin(25\pi t- 1.2)$ ? If so then use the fact that $sin(25\pi t- 1.2)= sin(25\pi)cos(1.2)- cos(25\pi t)sin(1.2)$ first.