y= x^3 sinx - 5cosc

To understand the equation y = x^3 sin(x) - 5cos(x), we need to break it down and explain each component:

1. x: This represents the independent variable of the equation. It can take any real value, and it will affect the value of y based on its relationship with the other terms.

2. x^3: The "x" raised to the power of 3 represents the cube of the value of x. This means that x is multiplied by itself three times.
- For example, if x = 2, then x^3 = 2^3 = 8.
- Similarly, if x = -3, then x^3 = (-3)^3 = -27.

3. sin(x): The sine function calculates the ratio of the length of the side opposite an angle in a right triangle to the hypotenuse.
- The sin(x) function oscillates between -1 and 1 as x varies.
- For instance, when x = 0, sin(0) = 0, and as x increases, sin(x) increases as well.

4. cos(x): The cosine function is similar to the sine function and calculates the ratio of the adjacent side to the hypotenuse in a right triangle.
- The cos(x) function also oscillates between -1 and 1, but with a different pattern than sin(x).
- For example, when x = 0, cos(0) = 1, and as x increases, cos(x) alternates between positive and negative values.

5. -5: This is a constant value that is subtracted from the product of x^3 and sin(x).
- It is a fixed number that affects the overall value of y in the equation.

Now, to evaluate y for a specific value of x, follow these steps:

1. Substitute the given value of x into the equation.
- For example, if x = 2, then y = (2^3)sin(2) - 5cos(2).

2. Calculate the value of x^3 by multiplying x by itself twice.
- In this case, x^3 = 2^3 = 8.

3. Calculate sin(x) and cos(x) for the given value of x, using a calculator or mathematical software.
- For x = 2, sin(2) ≈ 0.909 and cos(2) ≈ -0.416.

4. Substitute the values of x^3, sin(x), cos(x), and -5 into the equation and carry out the calculations.
- For x = 2, y = (8)(0.909) - (5)(-0.416) = 7.272 + 2.08 = 9.352.

Therefore, when x = 2, y is approximately equal to 9.352.