Question

-13cos2a если sina=-0.1

Answer 1

$Cos2\alpha=1-2Sin^{2}\alpha\\-13Cos2\alpha=-13(1-2Sin^{2}\alpha)=-13(1-2*0,1^{2})=-13(1-0,02)=-13*0,98=-12,74$

Answer 2

To find the value of the expression -13cos^2(a) when sin(a) = -0.1, we need to use some trigonometric identities. First, let's find the value of cos(a) using the given value of sin(a).

We know that sin^2(a) + cos^2(a) = 1

Given that sin(a) = -0.1, we can square both sides to get:

(-0.1)^2 + cos^2(a) = 1 0.01 + cos^2(a) = 1 cos^2(a) = 1 - 0.01 cos^2(a) = 0.99

Now, we can find the value of cos(a) by taking the square root of both sides:

cos(a) = ±√0.99

Since sin(a) is negative (-0.1), we know that a is in the 3rd or 4th quadrant of the unit circle, where cos(a) is also negative. Therefore, we take the negative value of the square root:

cos(a) = -√0.99 ≈ -0.9949874

Now, we can calculate the value of -13cos^2(a):

-13cos^2(a) = -13 * (-0.9949874)^2 -13cos^2(a) = -13 * 0.989995 -13cos^2(a) ≈ -12.869935

So, when sin(a) = -0.1, the value of -13cos^2(a) is approximately -12.869935.