Simplifying sin(3pi/2-x): An Exploration

[rachael]

What does "simplify" means in this case:
Simplify each of the following:
1. sin(3pi/2-x)

 

[VietDao29]

What does "simplify" means in this case:
Simplify each of the following:
1. sin(3pi/2-x)

Do you mean something like this:
$$\sin \left( \frac{3 \pi}{2 - x} \right)$$?
If you mean that, then I don't think it can be simplified any more.

 

[rachael]

nope i mean sin [(3pi/2)-x]

 

[VietDao29]

nope i mean sin [(3pi/2)-x]

Ahh, I see. I'll give you some hints. Do you know something like:
$$\sin (\pi + x) = - \sin x$$ and
$$\sin \left( \frac{\pi}{2} - x \right) = \cos x$$?

 

[HallsofIvy]

In other words, "simplify" here means "write in a simpler form" which would be something like Asin(x)+ Bcos(x) rather than sin($\theta$+x). In my opinion you would certainly be justified in arguing whether or not that is simpler but it is clearly what is intended.

 

[topsquark]

In general:
$$sin(A \pm B)=sinA \, cosB \pm sinB \, cosA$$
$$cos(A \pm B)=cosA \, cosB \mp sinA \, sinB$$

-Dan

 

[rachael]

thank you...