Пошаговое объяснение:
1) cosα = -0.8
π/2 <α<π ⇒ sinα >0
sin²α = 1 - 0.64 = 0.36
sinα = 0.6
tgα = -0.6/0.8 = -0.75
ctgα = 1/tgα = -4/3 = -1 1/3
2) cos240° + sin810° - tg150° = cos(60°+180°) + sin(90° + 2*360°) -tg(180°-30°) = - cos60° + sin90° + tg30° = -1/2 + 1 + √3/3 = √3/3 + 1/2
3) sin²α - sin⁴α + cos⁴α = sin²α(1 - sin²α)+ cos⁴α = sin²α*cos²α +cos⁴α = cos²α*(sin²α + cos²α) = cos²α
Пошаговое объяснение:
1) cosα = -0.8
π/2 <α<π ⇒ sinα >0
sin²α = 1 - 0.64 = 0.36
sinα = 0.6
tgα = -0.6/0.8 = -0.75
ctgα = 1/tgα = -4/3 = -1 1/3
2) cos240° + sin810° - tg150° = cos(60°+180°) + sin(90° + 2*360°) -tg(180°-30°) = - cos60° + sin90° + tg30° = -1/2 + 1 + √3/3 = √3/3 + 1/2
3) sin²α - sin⁴α + cos⁴α = sin²α(1 - sin²α)+ cos⁴α = sin²α*cos²α +cos⁴α = cos²α*(sin²α + cos²α) = cos²α