How do you simplify sin(x-pi/2)?

2 Answers
Aug 16, 2016

-cosx

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.

Dec 15, 2017

-cosx

Explanation:

The answer given prior is a perfectly valid explanation, but here is another:

We must consider our knowledge of transformations:

f(x-alpha) is a translation of f(x) by (alpha,0)

So hence:

sin(x- pi/2) is just sinx translated by (pi/2,0)

We see that sinx: graph{sinx [-4.006, 4.006, -2.003, 2.003]}

therefore sin(x-pi/2) : graph{sin(x- pi/2) [-4.006, 4.006, -2.003, 2.003]}

By observing this new graph, we see that this is just cosx reflected in the x axis

Hence just:

=> -cosx