Can I simplify \(\displaystyle{n}\cdot{r}\cdot{\sin{{\left({90}^{{\circ}}-{\frac{{{180}^{{\circ}}}}{{{n}}}}\right)}}}\sqrt{{{r}^{{2}}-{r}^{{2}}{{\sin}^{{2}}{\left({90}^{\circ}-{\frac{{{180}^{\circ}}}{{{n}}}}\right)}}}}\) further?

Damaris Huffman

Damaris Huffman

Answered question

2022-03-18

Can I simplify nrsin(90180n)r2r2sin2(90180n) further?

Answer & Explanation

Davin Thomas

Davin Thomas

Beginner2022-03-19Added 3 answers

n·r·sin(90°-180°n)r2-r2sin2(90°-180°n)
=nrcos(180n)r2r2cos2(180n)
=nrcos(180n)r2(1cos2(180n))
=nrcos(180n)r2sin2(180n)
=nrcos(180n)rsin(180n)
=nr2cos(180n)sin(180n)
=12nr2sin(360n)

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