Question

Вычислите sin319 cos109 - cos319 sin109

Answer 1

sin319 cos109 - cos319 sin109=sin(319-109)=sin(π+30)=-sin30=-1/2;

Answer 2

To calculate the value of the given expression, we need to use the trigonometric identities for the sum and difference of angles. Specifically, we'll use:

1. sin(a + b) = sin(a) * cos(b) + cos(a) * sin(b)
2. cos(a + b) = cos(a) * cos(b) - sin(a) * sin(b)

Let's use these identities to compute the expression sin(319) * cos(109) - cos(319) * sin(109):

sin(319) * cos(109) - cos(319) * sin(109) = sin(319 + 109) (Using identity 1) = sin(428) = sin(360 + 68) (Since sin(360 + x) = sin(x)) = sin(68)

So, the value of the expression is sin(68). To get the numerical value, we can use a calculator or a trigonometric table. On most calculators, trigonometric functions take angles in degrees, not radians.

Using a calculator, sin(68) ≈ 0.897927.

Therefore, sin(319) * cos(109) - cos(319) * sin(109) ≈ 0.897927.