Question

3 cos(П/2+a)+2sin(п-а) если sin a=0,6

Answer 1

Нужно воспользоваться формулами приведения:
cos(π/2 + α) = -sin α, sin(π - α) = sin α.
3cos(π/2 + α) + 2sin(π - α) = -3sinα + 2sinα = -sinα = -0,6

Answer 2

To simplify the expression, we'll substitute the value of sin(a) and use trigonometric identities to simplify further. Given that sin(a) = 0.6, we can calculate cos(a) using the identity cos^2(a) + sin^2(a) = 1:

cos^2(a) = 1 - sin^2(a) cos^2(a) = 1 - 0.6^2 cos^2(a) = 1 - 0.36 cos^2(a) = 0.64

Taking the square root of both sides, we get:

cos(a) = ±√0.64

Since sin(a) is positive (0.6), cos(a) must also be positive. Therefore:

cos(a) = √0.64 cos(a) = 0.8

Now, we can substitute the values of sin(a) and cos(a) into the expression:

3 cos(π/2 + a) + 2 sin(π - a)

= 3 cos(π/2) cos(a) - 3 sin(π/2) sin(a) + 2 sin(π) cos(a) - 2 cos(π) sin(a)

Using the values of cos(π/2) = 0, sin(π/2) = 1, sin(π) = 0, and cos(π) = -1, we have:

= 3 * 0 * 0.8 - 3 * 1 * 0.6 + 2 * 0 * 0.8 - 2 * (-1) * 0.6

= 0 - 1.8 + 0 + 1.2

= -0.6

Therefore, the value of the expression 3 cos(π/2 + a) + 2 sin(π - a) when sin(a) = 0.6 is -0.6.