How do you simplify sin(x-pi/2)?
2 Answers
Explanation:
Using the appropriate
color(blue)"addition formula"
color(orange)"Reminder"
color(red)(|bar(ul(color(white)(a/a)color(black)(sin(A-B)=sinAcosB-cosAsinB)color(white)(a/a)|)))
rArrsin(x-pi/2)=sinxcos(pi/2)-cosxsin(pi/2) now
cos(pi/2)=0" and " sin(pi/2)=1
rArrsin(x-pi/2)=sinx(0)-cosx(1)=-cosx This is a useful result and worth knowing for future reference.
Explanation:
The answer given prior is a perfectly valid explanation, but here is another:
We must consider our knowledge of transformations:
So hence:
We see that
By observing this new graph, we see that this is just
Hence just: