Question

2sin(-П/4)cosП\4+sinП+2cos(-П/3)

Answer 1

Ответ:

√18.

Пошаговое объяснение:

Учитывая знаки тригонометрических функции в координатных четвертях, а также, значения синуса и косинуса для углов 0; π/3; π/4; π/6; π/2; π, вычислим:

а) sin (- π/4) + cos π/3 + cos (- π/6) = - √2/2 +1/2 - √3/2 = (-√2 + 1 - √3)/2.

б) sin (- 3П/2) - cos (-П ) + sin ( - 3П/2)  = 1 – 1 + 0 = 0 ,

в) 2 sin 0 + 3 sin П/2 - 4 sin П/2 = 0 + 3 * 1 - 4 * 1= -1.

г) sin (- П/2) - cos (- П) + sin (- 3П/2) = -1 + 1 – 1 = -1 ,

д) cos П/6 * cos П/4 * cos П/3 * cos П/2 * cos 2П/3 = √3 * √2 * 1/2 * 0 * (-1/2) = 0 ,

е) sin П/6 * sin П/4 * sin П/3 * sin П/2 * sin 2П/3 = 1/2 * √2/2 * √3/2 * 1 * √3/2 =

= (1 * √2 * √3 * 2 * √3)/2 = (2 * √2 * √3 * √3)/2 = √18.

Answer 2

It appears that you want to simplify the expression:

2sin(-π/4)cos(π/4) + sin(π) + 2cos(-π/3)

Let's break it down step by step:

1. First, let's simplify the trigonometric values:

sin(-π/4) = -sin(π/4) cos(π/4) = cos(π/4) cos(-π/3) = cos(π/3)

2. Plug these simplified values back into the expression:

2(-sin(π/4)cos(π/4)) + sin(π) + 2cos(π/3)

3. Now, let's compute the trigonometric values:

sin(π/4) = 1/√2 cos(π/4) = 1/√2 sin(π) = 0 (sine of π is 0) cos(π/3) = 1/2

4. Plug these values back into the expression:

2(-1/√2 * 1/√2) + 0 + 2(1/2)

5. Simplify further:

-1/2 + 0 + 1 = 1/2

So, the simplified expression is 1/2.