Question

Sin(3 arctg корень из 3+arccos 1/2)

Answer 1

Ответ:

Пошаговое объяснение:

Sin(3 arctg корень из 3+arccos 1/2)

3arctg√3=3*п/3=п

arccos 1/2=п/3

Sin(п+п/3)=-sin(п/3)=-(√3)/2

Answer 2

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

1. Let's start with the innermost expression: arccos(1/2). The cosine of an angle is equal to 1/2 when the angle is 60 degrees or π/3 radians. Therefore, arccos(1/2) = π/3.

2. Now let's move on to the next part: √3 + arccos(1/2). Substituting the value we found for arccos(1/2), we have √3 + π/3.

3. Finally, we have sin(3 arctg (√3 + arccos(1/2))). Using the angle addition formula for tangent, we can rewrite it as sin(3(arctg(√3) + arctg(π/3))).

   The tangent of an angle is equal to the ratio of the sine and cosine of the angle. For arctg(√3), the tangent is 1, and for arctg(π/3), the tangent is also 1. Therefore, we can simplify it further to sin(3(1 + 1)).

4. Simplifying further, we have sin(6), where 6 is the sum of the two tangent values.

The sine of 6 radians is approximately 0.279.