Question Number 130632 by bramlexs22 last updated on 27/Jan/21
Answered by EDWIN88 last updated on 27/Jan/21
$$\mathrm{cos}\:\mathrm{4095}°\:=\:\mathrm{cos}\:\left(\mathrm{360}°×\mathrm{11}+\mathrm{135}°\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:−\frac{\sqrt{\mathrm{2}}}{\mathrm{2}} \\ $$$${then}\:\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{cos}\:\mathrm{4095}°\right)=\mathrm{sin}\:\left(−\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\right) \\ $$$$\:=−\frac{\pi}{\mathrm{4}} \\ $$