Question

Sin(a+β)- sina·cosβ,если cosa=0,6,f sinaβ=0,8 а)1,4 б)-0,2 в)0,48 г)-0,48

Answer 1

Sin a+b = sina * cosb + sinb*cosa
из cosa = 0.6 находим sin a по тригонометрическому тождеству, sina=(1-(cosa)^2)^1/2 
И такую же операцию с sinb , cosb = (1-(sinb)^2)^1/2
Получаем sina = 0.8
cos b = 0.6
Подставляем получившееся в выражение: 0.8*0.6 +0.8* 0.6 -0.8*0.6 = 0.48

Answer 2

To find the value of the expression sin(a + β) - sin(a) · cos(β), we first need to determine the values of sin(a) and cos(β) using the given information:

Given:

1. cos(a) = 0.6
2. sin(aβ) = 0.8

We can use the Pythagorean identity: sin²(θ) + cos²(θ) = 1 to find sin(a):

sin²(a) + cos²(a) = 1 sin²(a) + (0.6)² = 1 sin²(a) + 0.36 = 1 sin²(a) = 1 - 0.36 sin²(a) = 0.64 sin(a) = √(0.64) sin(a) = 0.8

Now, we can find cos(β):

sin(aβ) = 0.8 cos(β) = ±√(1 - sin²(β)) cos(β) = ±√(1 - 0.64) cos(β) = ±√(0.36) cos(β) = ±0.6

Since sin(aβ) is positive (0.8) and cos(a) is positive (0.6), we can choose the positive value for cos(β):

cos(β) = 0.6

Now we can find the value of the expression:

sin(a + β) - sin(a) · cos(β) = sin(a) · cos(β) + cos(a) · sin(β) - sin(a) · cos(β)

Since sin(a) = 0.8 and cos(β) = 0.6, we get:

sin(a + β) - sin(a) · cos(β) = 0.8 · 0.6 + 0.6 · 0.8 - 0.8 · 0.6 sin(a + β) - sin(a) · cos(β) = 0.48 + 0.48 - 0.48 sin(a + β) - sin(a) · cos(β) = 0

So, the correct answer is:

в) 0