Question

3sina - 5cosa/5sina+3cosa если tga=-4/9
помогите решить. очень нужно!!

Answer 1

Ответ:

To solve this problem, we can use the following trigonometric identities:

sin²θ + cos²θ = 1

tanθ = sinθ/cosθ

We are given that tan(a) = -4/9, and we want to find the value of:

3sin(a) - 5cos(a) / 5sin(a) + 3cos(a)

First, we can use the identity tan(a) = sin(a)/cos(a) to find the values of sin(a) and cos(a):

tan(a) = sin(a)/cos(a)

sin(a) = tan(a) * cos(a)

cos(a) = 1/sqrt(1 + tan²(a))

Plugging in the value of tan(a) = -4/9, we get:

sin(a) = (-4/9) * cos(a)

cos(a) = 1/sqrt(1 + (-4/9)²) = 9/sqrt(97)

Next, we can substitute these values into the expression we want to evaluate:

3sin(a) - 5cos(a) / 5sin(a) + 3cos(a) = 3*(-4/9)cos(a) - 5(9/sqrt(97))cos(a) / 5(-4/9)sin(a) + 3(9/ sqrt(97))*sin(a)

Simplifying this expression, we get:

(-12sqrt(97) - 45)/(-20sqrt(97) + 36) = (45 + 12sqrt(97))/(20sqrt(97) - 36)

Therefore, the value of the expression is (45 + 12sqrt(97))/(20sqrt(97) - 36), given that tan(a) = -4/9.