From where does this - ve sign come from

Question

Let
θ=54
5θ=270
2θ+3θ=270
2θ=270-3θ
sin(2θ)=sin(270-3θ)
sin(2θ)= -cos(3θ)
From where does -ve sign come from?

270-3θ will be in 2quad where sin is +ve.

Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. — José Carlos Santos, Nov 28 '18 at 06:47
@EeveeTrainer "-ve" and "+ve" are shorthands for "negative" and "positive", respectively. — , Nov 28 '18 at 06:57
Huh; never seen that before and nothing came up when I Googled it. Thanks. — PrincessEev, Nov 28 '18 at 07:01

score 2 · Answer 1 · answered Nov 28 '18 at 06:42

2

\begin{align} \sin (270^\circ-\alpha) &= \sin(270^\circ)\cos(\alpha) -\cos(270^\circ) \sin(\alpha) \\ &=- \cos (\alpha) \end{align}

answered Nov 28 '18 at 06:42

Siong Thye Goh

score 0 · Answer 2 · answered Nov 28 '18 at 06:43

0

$\sin(-90^\circ -\alpha) = \cos(\alpha)$ for any $\alpha$

answered Nov 28 '18 at 06:43

Fareed Abi Farraj

2 Answers2