Question

Найдите -20cos2a, если sin= - 0,8

Answer 1

-20Cos2a=-20(1-2Sin²a)=-20×(1-2×0,64)=-20×(-0,28)=5,6

Answer 2

To find the value of -20cos(2a), we need to first find the value of cos(2a) using the given information that sin(a) = -0.8. Here's how we can do it:

1. Recall the Pythagorean identity: sin^2(a) + cos^2(a) = 1

2. Square the given sin(a) value: (-0.8)^2 + cos^2(a) = 1 0.64 + cos^2(a) = 1

3. Solve for cos^2(a): cos^2(a) = 1 - 0.64 cos^2(a) = 0.36

4. Now, find the value of cos(a) (we use the positive value because sin(a) is negative, which means a is in the third or fourth quadrant where cos(a) is positive): cos(a) = √(0.36) cos(a) = 0.6

5. Now, to find cos(2a), we can use the double-angle formula for cosine: cos(2a) = 2cos^2(a) - 1 cos(2a) = 2(0.6)^2 - 1 cos(2a) = 2(0.36) - 1 cos(2a) = 0.72 - 1 cos(2a) = -0.28

6. Finally, to find -20cos(2a): -20cos(2a) = -20 * (-0.28) -20cos(2a) = 5.6

So, -20cos(2a) equals 5.6.