Question

Cos(4п-п/3)+sin(п/6+п)

Answer 1

Решаем по формулам приведения.

Answer 2

To simplify the given expression, let's break it down step by step:

1. Cos(4π - π/3): We know that cos(x) is periodic with a period of 2π. So, we can subtract 2π from the given angle until we get an angle within the range [0, 2π].

   4π - π/3 = (12π/3) - (π/3) = (12π - π) / 3 = 11π / 3

   Now, we need to find the value of cosine for the angle 11π / 3.

2. Sin(π/6 + π): π/6 + π = (π + 6π)/6 = 7π/6

   Now, we need to find the value of sine for the angle 7π/6.

Using the unit circle or a calculator, we can determine the values of cosine and sine for the respective angles:

1. Cos(11π/3) ≈ -0.5
2. Sin(7π/6) ≈ -0.5

Now, we can substitute the values back into the expression:

Cos(4π - π/3) + Sin(π/6 + π) ≈ -0.5 + (-0.5) = -1

Therefore, the simplified value of the given expression is -1.