Question

Найдите -7cos2a, если sina=-0,5

Answer 1

Ответ:

= - 7,5

Пошаговое объяснение:

$cos2 \: a = 1 - 2 {sin}^{2} a$

$cos2a = 1 - 2 \times {( - 0.5)}^{2}$

-7 cos2 a=-7-0,5=-7,5

Answer 2

To find the value of -7cos(2a) when sin(a) = -0.5, we need to determine the value of cos(2a).

We know that sin(a) = -0.5, which means that a is in the third or fourth quadrant since sin is negative in those quadrants. Let's assume a is in the third quadrant.

sin(a) = -0.5 By using the Pythagorean identity sin^2(a) + cos^2(a) = 1, we can calculate cos(a): (-0.5)^2 + cos^2(a) = 1 0.25 + cos^2(a) = 1 cos^2(a) = 0.75 cos(a) = ±√0.75

Since a is in the third quadrant, cos(a) is negative: cos(a) = -√0.75

Now, we need to find cos(2a): cos(2a) = 2cos^2(a) - 1

Substituting the value of cos(a): cos(2a) = 2(-√0.75)^2 - 1 cos(2a) = 2(0.75) - 1 cos(2a) = 1.5 - 1 cos(2a) = 0.5

Finally, we can calculate -7cos(2a): -7cos(2a) = -7(0.5) -7cos(2a) = -3.5

Therefore, when sin(a) = -0.5, the value of -7cos(2a) is -3.5.