1) 12sin810°; 2) 18cos600°; 3) 51√2sin315°; 4) 38√2cos675°; 5) 40√3sin840°; 6) 24√3cos570°; 7) tg61°ctg61°; 8) tg154°ctg154°.

Question

Accepted Answer

\( 12\sin{810°} = 12\sin{(810° - 2 × 360°)} = 12\sin{90°} = 12 × 1 = 12 \)
\( 18\cos{600°} = 18\cos{(600° - 360°)} = 18\cos{240°} = 18(-\frac{1}{2}) = -9 \)
\( 51\sqrt{2}\sin{315°} = 51\sqrt{2}\sin{(360° - 45°)} = 51\sqrt{2}(-\sin{45°}) = 51\sqrt{2}(-\frac{\sqrt{2}}{2}) = -51 \)
\( 38\sqrt{2}\cos{675°} = 38\sqrt{2}\cos{(675° - 360°)} = 38\sqrt{2}\cos{315°} = 38\sqrt{2}\cos{(360° - 45°)} = 38\sqrt{2}\cos{45°} = 38\sqrt{2}\frac{\sqrt{2}}{2} = 38 \)
\( 40\sqrt{3}\sin{840°} = 40\sqrt{3}\sin{(840° - 2 × 360°)} = 40\sqrt{3}\sin{120°} = 40\sqrt{3}\frac{\sqrt{3}}{2} = 60 \)
\( 24\sqrt{3}\cos{570°} = 24\sqrt{3}\cos{(570° - 360°)} = 24\sqrt{3}\cos{210°} = 24\sqrt{3}(-\frac{\sqrt{3}}{2}) = -36 \)
\( \text{tg}61°\text{ctg}61° = 1 \)
\( \text{tg}154°\text{ctg}154° = 1 \)

Ответ: 1) 12; 2) -9; 3) -51; 4) 38; 5) 60; 6) -36; 7) 1; 8) 1.