Unit Cirlce Trigonometry

$\text{Probably the clearest way to do this is to note that}\\ \cos(\angle RPS)=\cos\left(\pi - \angle RPQ\right)=-\cos(\angle RPQ)\\ \cos(\angle RPQ)=\sqrt{1 -\sin^2(\angle RPQ)} = \sqrt{1-\frac{49}{625}} \\ \cos(\angle RPQ) = \sqrt{\dfrac{576}{625}}=\dfrac{24}{25},\text{ and thus}\\ \cos(\angle RPS)=-\dfrac{24}{25}$

Thank you rom once again