Удачник66
A ∈ [pi; 3pi/2] - 3 четверть, sin a < 0; cos a < 0 sin a = -15/17; cos a = -√(1 - sin^2 a) = -√(1 - 225/289) = -√(64/289) = -8/17 b ∈ [3pi/2; 2pi] - 4 четверть, sin b < 0; cos b > 0 cos b = 8/17; sin b = -√(1 - cos^2 b) = -√(1 - 64/289) = -√(225/289) = -15/17 cos(a + b) = cos a*cos b - sin a*sin b = -8/17*8/17 - (-15/17)(-15/17) = = -64/289 - 225/289 = -1 cos(a + b) = -1 a + b = pi
Answers & Comments
sin a = -15/17; cos a = -√(1 - sin^2 a) = -√(1 - 225/289) = -√(64/289) = -8/17
b ∈ [3pi/2; 2pi] - 4 четверть, sin b < 0; cos b > 0
cos b = 8/17; sin b = -√(1 - cos^2 b) = -√(1 - 64/289) = -√(225/289) = -15/17
cos(a + b) = cos a*cos b - sin a*sin b = -8/17*8/17 - (-15/17)(-15/17) =
= -64/289 - 225/289 = -1
cos(a + b) = -1
a + b = pi