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Question Number 130632 by bramlexs22 last updated on 27/Jan/21

Answered by EDWIN88 last updated on 27/Jan/21

cos 4095° = cos (360°×11+135°)                      = −((√2)/2)  then sin^(−1) (cos 4095°)=sin (−((√2)/2))   =−(π/4)

$$\mathrm{cos}\:\mathrm{4095}°\:=\:\mathrm{cos}\:\left(\mathrm{360}°×\mathrm{11}+\mathrm{135}°\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:−\frac{\sqrt{\mathrm{2}}}{\mathrm{2}} \\ $$$${then}\:\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{cos}\:\mathrm{4095}°\right)=\mathrm{sin}\:\left(−\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\right) \\ $$$$\:=−\frac{\pi}{\mathrm{4}} \\ $$

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