Тригонометрия 10 класс

84) 5sin(a - 7pi) - 11cos(a + 3pi/2) = 4
sin(a - 7pi) = sin(a - pi) = -sin(pi - a) = -sina
cos(a + 3pi/2) = cos(a - pi/2) = cos(pi/2 - a) = sina
-5sina - 11sina = -5*(-0.25) - 11*(-0.25) = 4
85) (3cosa - 4sina) / (2sina - 5cosa) = -9
tga = sina/cosa = 3, sina = 3cosa
(3cosa - 4*3cosa) / (2*3cosa - 5cosa) = -9cosa/cosa = -9
86) (10cosa + 4sina + 15) / (2sina + 5cosa + 3) = 5
tga = sina/cosa = -2.5, sina = -2.5cosa
(10cosa - 4*2.5cosa + 15) / (-2*2.5cosa + 5cosa + 3) = 15 / 3 = 5
87) 26cos(a + 3pi/2) = 26cos(a - pi/2) = 26cos(pi/2 - a) = 26sina = -10
cosa = 12/13, a - в 4 четверти
sina lt; 0, sina = -sqrt(1 - cos^2(a)) = -sqrt(25/13^2) = -5/13
26*(-5/13) = -10
88) sina(7pi/2 - a) = sin(pi/2 - a) = cosa = -0.6
sina = 0.8, a - в 2 четверти
cosa lt; 0, cosa = -sqrt(1 - sin^2(a)) = -0.6
89) 24cos(2a) = 24*(1 - 2sin^2(a)) = 22.08
sina = -0.2
sin^2(a) = 0.04
24*(1 - 2*0.04) = 24*(1 - 0.08) = 24*0.92 = 22.08
90) tga = sina/cosa = 5
sina = -5/sqrt26, a - в 3 четверти
cosa lt; 0, cosa = -sqrt(1 - sin^2(a)) = -1/sqrt26
(-5/sqrt26) / (-1/sqrt26) = 5