Question Number 12705 by @ANTARES_VY last updated on 29/Apr/17
$$\boldsymbol{\mathrm{this}}\:\:\boldsymbol{\mathrm{y}}=\boldsymbol{\mathrm{sin}}\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\:\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{range}}\:\:\boldsymbol{\mathrm{of}} \\ $$$$\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{function}}. \\ $$
Answered by Joel577 last updated on 29/Apr/17
$$\mathrm{Range} \\ $$$$−\mathrm{1}\:\leqslant\:{y}\:\leqslant\:\mathrm{1} \\ $$
Commented by @ANTARES_VY last updated on 29/Apr/17
$$\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{does}}\:\:\boldsymbol{\mathrm{it}}\:\:\boldsymbol{\mathrm{work}}? \\ $$
Commented by arnabpapu550@gmail.com last updated on 09/Jun/17
![As range of sinθ , cosθ ∈[−1,+1] ∴ sin(x/2)∈[−1,+1]](https://www.tinkutara.com/question/Q15321.png)
$$\mathrm{As}\:\mathrm{range}\:\mathrm{of}\:\mathrm{sin}\theta\:,\:\mathrm{cos}\theta\:\in\left[−\mathrm{1},+\mathrm{1}\right] \\ $$$$\therefore\:\mathrm{sin}\frac{\mathrm{x}}{\mathrm{2}}\in\left[−\mathrm{1},+\mathrm{1}\right] \\ $$