Question

Вычислите 100sin2a, если cosa = -0.8 и pi/2<a<pi​

Answer 1

$cosa=-0,8\\\\\frac{\pi}{2}$

Answer 2

To find the value of 100sin^2(a) given that cos(a) = -0.8 and π/2 < a < π, we can follow these steps:

Step 1: Use the Pythagorean trigonometric identity to find sin(a). Step 2: Square sin(a) to get sin^2(a). Step 3: Multiply sin^2(a) by 100 to get the final result.

Let's proceed with the calculations:

Step 1: Since cos(a) = -0.8 and π/2 < a < π, we are in the second quadrant, where the sine function is positive. We can use the Pythagorean trigonometric identity:

sin^2(a) + cos^2(a) = 1

Substitute cos(a) = -0.8:

sin^2(a) + (-0.8)^2 = 1

sin^2(a) + 0.64 = 1

sin^2(a) = 1 - 0.64

sin^2(a) = 0.36

Step 2: Now, we have the value of sin^2(a), which is 0.36.

Step 3: Finally, multiply sin^2(a) by 100 to get the answer:

100 * sin^2(a) = 100 * 0.36 = 36

So, 100sin^2(a) is equal to 36.