Question

Cos(3π/2 - 0.5x)=0.5

Answer 1

Cos(3π/2 - 0.5x) = 0.5
-cos 0.5x = 0.5
cos 0.5x = -0.5
1) 0.5x = 2π/3 + 2πk → x1 = 4π/3 + 4πk
2) 0.5x = -2π/3 + 2πk → x2 = -4π/3 + 4πk
Ответ: х = +- 4π/3 + 4πk  (k∈Z)

Answer 2

To find the value of x that satisfies the equation cos(3π/2 - 0.5x) = 0.5, we can use inverse trigonometric functions.

First, let's rewrite the equation in terms of an inverse cosine function:

cos(3π/2 - 0.5x) = 0.5

Taking the inverse cosine of both sides, we get:

3π/2 - 0.5x = arccos(0.5)

Now, let's solve for x:

0.5x = 3π/2 - arccos(0.5)

To isolate x, divide both sides of the equation by 0.5:

x = (3π/2 - arccos(0.5)) / 0.5

Using a calculator to evaluate the right-hand side of the equation, we can determine the value of x.