cost=15/17
sin²t+cos²t=1
Так как угол t принадлежит четвертой четверти, sint < 0
sint=√(1-cos²t)
sint=√((289-225)/289) = √(64/289) = - 8/17
tgt = sint/cost = - 8/15
ctgt = 1/tgt = - 15/8
Давай сделаем по частям, по кусочкам и будет понятно.
а) 81 = 3^4
81^-0,75 = (3^4)^-0,75= 3^(4·(-0,75))= 3^-3 = 1/27
125 = 5^3
(1/5^3)^1/3= 1/5^(3·1/3) = 1/5
32 = 2^5
1/(2^5)1/5= 1/2
Сам пример: 1/27 + 1/5 - 1/2 = 10/270 + 54/270 - 135/270 = -71/270
б) 27= 3^3
27^2/3 = (3^3)^2/3= 3^(3·2/3) = 3^2 = 9
16= 2^4
1/16^-0,75 = 1/(2^4)^-0,75 = 1/2^(4·(-0,75))=1/2^3= 1/8
25^0,5= (5^2)^0,5 = 5^(2·0,5) = 5
Сам пример: 9 + 1/8 - 5 = 4 1/8
cos(t - π/3) = cost * cos pi/3 + sint *sin pi/3
cos pi/3= 1/2
sin pi/3= <span><span><span><span>√</span></span></span></span>3/2
cos^2t+sin^2t=1 - тригометрическое тождество
sin^2t=1-cos^2t
sint= 15/17 - неподходит, тк t ∈ (π; 3π/2).
sint= -15/17
cos(t - π/3) = cost * cos pi/3 + sint *sin pi/3 = -8/17 * 1/2 + 15/17 * <span><span><span><span>√</span></span></span></span>3/2 =
-8/24+ 15<span><span><span><span>√</span></span></span></span>3/24 = (15<span><span><span><span>√</span></span></span></span>3-8) / 24
Ответ: (15<span><span><span><span>√</span></span></span></span>3-8) / 24
√(9*16) = 3 * 4 = 12
√(36*81) = 6*9 = 54
√(0,01*0,49)= 0,1*0,7 = 0,07
√(0,16*1,96) = 0,4*1,4 = 0,56
