Question

3/4sin(2П+a)-sin(3П+a) Если a=П/4

Answer 1

Ответ:(7*2^(1/2))/8

Пошаговое объяснение:

Answer 2

To evaluate the expression 3/4 * sin(2П + a) - sin(3П + a) when a = П/4, we simply substitute the value of a into the expression and perform the calculations. Let's do that step by step:

1. Substitute a = П/4 in the expression: 3/4 * sin(2П + П/4) - sin(3П + П/4)

2. Calculate the angles inside the sine function: sin(2П + П/4) = sin(8П/4 + П/4) = sin(9П/4) sin(3П + П/4) = sin(12П/4 + П/4) = sin(13П/4)

3. Substitute back into the expression: 3/4 * sin(9П/4) - sin(13П/4)

4. Since sin(9П/4) and sin(13П/4) are negative, we can write them in terms of positive angles (in the unit circle, sin is positive in the first and second quadrants): sin(9П/4) = -sin(П/4) sin(13П/4) = -sin(П/4)

5. Now, substitute back into the expression again: 3/4 * (-sin(П/4)) - (-sin(П/4))

6. Distribute the 3/4 factor: -3/4 * sin(П/4) + sin(П/4)

7. Combine like terms: (-3/4 + 1) * sin(П/4) = -1/4 * sin(П/4)

So, the final simplified expression is: -1/4 * sin(П/4)