Question

Известно что cos a= - 0,6, П <а<3п/2 найти значение sin a

Answer 1

Sin a= √(cos^2-1)
sin a= √((-0.6)-1)= √( 36/100- 1) = √(64/100)=+- 8/10=+- 0.8, т.к.а принадлежит 3 четверти, где он отрицательный, значить выбираем с минусом: - 0,8))))

Answer 2

To find the value of sin(a) when cos(a) = -0.6 and a is in the range of π/2 < a < 3π/2, we can use the Pythagorean trigonometric identity, which states:

sin^2(a) + cos^2(a) = 1

Given that cos(a) = -0.6, we can calculate sin(a) as follows:

sin^2(a) + (-0.6)^2 = 1

sin^2(a) + 0.36 = 1

sin^2(a) = 1 - 0.36

sin^2(a) = 0.64

Now, take the square root of both sides to find sin(a):

sin(a) = ±√(0.64)

However, since we know that a is in the range of π/2 < a < 3π/2, sin(a) is negative in this interval. So, we take the negative value:

sin(a) = -√(0.64) = -0.8

Therefore, the value of sin(a) is -0.8.