Answer:
[tex]cos(x-\frac{3\pi }{2} )= \frac{-3}{4} cos(x)[/tex]
Step-by-step explanation:
Lets remember the following expression:
cos(x-a)= cos(x)*cos(a)+sin(x)*sin(a)
if a= -3 pi /2 then:
cos(x-3 pi/2)= cos(x)*cos(3pi/2) + sin(x)*sin(3pi/2)
Since cos (3pi/2) is located exactly at 'y' axis, its value=0
Moreover sin(3pi/2)= -1 because, that angle is located at 'y' axis, negative side
cos(x-3pi/2)= -sin(x)
But, we can simplify a little more since we now that tan(x)=3/4
That means that sin(x)/cos(x)= 3/4, from that expression we isolate sin(x) and we obtain that sin(x)=cos(x) * 3/4
Using the above conclusion we have that
cos(x-3pi/2)= -cos(x)*3/4
