Why doesn't Simplify[Sqrt[(Sin[a])^2] ] give Sin[a]?

Question

I am getting Sqrt[Sin[a]^2] as the output to a calculation and I want it to be displayed as Sin[a].

(1) Sqrt[sin^2(a)] is not proper syntax. (2) Sqrt[u^2] does not equal u, even for the real numbers, much less for complex numbers, which is the domain Mathematica works over. You could try Simplify[Sqrt[(sin (a))^2], sin (a) > 0], which yields a sin, an equivalent form of sin(a), according to Mathematica syntax. Probably you want Simplify[Sqrt[Sin[a]^2], Sin[a] > 0] and to learn the syntax of Mathematica. — Michael E2, Jul 18 '17 at 20:58
You can use PowerExpand to do this simplification, but you should be sure that this is the right thing to do (see @JohnDoty's answer). — JEM_Mosig, Jul 19 '17 at 01:54

score 4 · Answer 1 · answered Jul 18 '17 at 21:01

4

Well, proper syntax would help. Then note that

Sqrt[Sin[a]^2] /. a -> -I
(* I Sinh[1] *)

but

Sin[a] /. a -> -I
(* -I Sinh[1] *)

answered Jul 18 '17 at 21:01

John Doty

I see. I'm not familiar with the syntax /. a -> -I What does it mean? – Leo Jul 19 '17 at 00:40
1

Look up Replace in the documentation. – John Doty Jul 19 '17 at 00:54
@AdwaitMane There's a compendium for such symbols here – Michael E2 Jul 19 '17 at 00:56
Got it. Thanks. – Leo Jul 19 '17 at 11:58
I was able to get the desired form by restricting a to the reals. Simplify[Sqrt[(Sin[a])^2], -Infinity < a < Infinity] gives |Sin[a]|. – Leo Jul 19 '17 at 12:05

1 Answers1