Certainly! Let's go through the problem step-by-step to find the function [tex]\( y \)[/tex] given by [tex]\( y = \sin^3(4x + 10) \)[/tex].
### Step 1: Recognize the Inner Function
First, observe that the inner function inside the sine function is [tex]\( 4x + 10 \)[/tex].
### Step 2: Apply the Sine Function
Next, apply the sine function to this inner function to get:
[tex]\[ \sin(4x + 10) \][/tex]
### Step 3: Cube the Sine Function Result
Finally, take the result of the sine function and raise it to the power of 3. In mathematical terms, it becomes:
[tex]\[ y = \left( \sin(4x + 10) \right)^3 \][/tex]
### Final Expression
Putting it all together, the function [tex]\( y \)[/tex] is expressed as:
[tex]\[ y = \sin^3(4x + 10) \][/tex]
So, the detailed step-by-step solution gives us:
[tex]\[ y = \sin^3(4x + 10) \][/tex]
This is the required expression for [tex]\( y \)[/tex].
