Kelton Rogers

2023-03-25

Find the value of $\mathrm{sin}{270}^{\circ}$.

Bollacasaep22

Beginner2023-03-26Added 6 answers

Find the value given trigonometric expression.

We know, $\mathrm{sin}{270}^{\circ}$can be stated as, $\mathrm{sin}{270}^{\circ}=\mathrm{sin}({180}^{\circ}+{90}^{\circ})$

As $\mathrm{sin}$ is a periodic function of time period $2\pi $, also negative in third quadrant or $\mathrm{sin}(\pi +\theta )=-\mathrm{sin}\theta $,where$\pi ={180}^{\circ}$

Hence,

$\mathrm{sin}{270}^{\circ}=\mathrm{sin}({180}^{\circ}+{90}^{\circ})=-\mathrm{sin}{90}^{\circ}=-1\therefore \mathrm{sin}{270}^{\circ}=-1$

Thus, the value of $\mathrm{sin}{270}^{\circ}$is$-1$.

We know, $\mathrm{sin}{270}^{\circ}$can be stated as, $\mathrm{sin}{270}^{\circ}=\mathrm{sin}({180}^{\circ}+{90}^{\circ})$

As $\mathrm{sin}$ is a periodic function of time period $2\pi $, also negative in third quadrant or $\mathrm{sin}(\pi +\theta )=-\mathrm{sin}\theta $,where$\pi ={180}^{\circ}$

Hence,

$\mathrm{sin}{270}^{\circ}=\mathrm{sin}({180}^{\circ}+{90}^{\circ})=-\mathrm{sin}{90}^{\circ}=-1\therefore \mathrm{sin}{270}^{\circ}=-1$

Thus, the value of $\mathrm{sin}{270}^{\circ}$is$-1$.

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