Question

Find the exact value of each expression. sin0 , if cos 0 =3/5 and 270° ≤0 ≤360°

Answer 1

$\text{Given that,}\\\\~~~~~~~~\cos \theta = \dfrac 35\\\\\implies \cos^2 \theta = \dfrac 9{25}\\\\\implies 1-\sin^2 \theta = \dfrac{9}{25}\\\\\implies \sin^2 \theta = 1-\dfrac{9}{25}\\\\\implies \sin^2 \theta = \dfrac{16}{25}\\\\\implies \sin \theta = \pm\sqrt{\dfrac{16}{25}}\\\\\implies \sin \theta = \pm\dfrac 45\\\\\text{Given that,}~ 270^{\circ} \leq \theta \leq 360^{\circ}, \text{So}~ \theta ~ \text{lies in fourth quadrant.}$

$\text{Which means that}~ \sin \theta ~ \text{will be negative.}\\\\\text{Hence,}~ \sin \theta = -\dfrac 45$