Question

Найти значение cos a, если sin a = - 4/5 и п < а < 3п/2

Answer 1

Ответ: cos a =(1-(sin a)^2)=(1-16/25)^0,5=(9/25)^0,5=-3/5 c учётом диапазона углов.

Объяснение:

Answer 2

To find the value of cos(a) given that sin(a) = -4/5 and π < a < 3π/2, we can use the Pythagorean trigonometric identity:

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

Given sin(a) = -4/5, we can find cos(a) using the above identity.

sin^2(a) = (-4/5)^2 = 16/25

Now, substituting this value in the Pythagorean identity:

cos^2(a) = 1 - sin^2(a) = 1 - 16/25 = 9/25

Taking the square root of both sides:

cos(a) = ± √(9/25) = ± 3/5

Now, we need to determine whether cos(a) is positive or negative based on the given interval π < a < 3π/2.

Since the sine is negative (sin(a) = -4/5), it indicates that a is in the third quadrant or the fourth quadrant. In both of these quadrants, the cosine function is negative.

So, cos(a) = -3/5.