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 = \frac 35\\\\\implies \cos^2 \theta = \frac 9{25}\\\\\implies 1-\sin^2 \theta = (9)/(25)\\\\\implies \sin^2 \theta = 1-(9)/(25)\\\\\implies \sin^2 \theta = (16)/(25)\\\\\implies \sin \theta = \pm\sqrt{(16)/(25)}\\\\\implies \sin \theta = \pm\frac 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 = -\frac 45`