Distributing Cos45 in an Expression: Numerator and Denominator

[Ryuk1990]

Let's say I have an expression like this.

cos45[(601-148)/sin21.8]

Does cos45 get multiplied into just the numerator terms or do I also distribute it to the denominator as well?

 

[n!kofeyn]

Only the numerator. Think of it as cos(45)/1 so that cos(45) multiplies the numerator and 1 multiples the denominator.

Also, notice that cos(45) equals something simple.

 

[Pengwuino]

Multiplying into the numerator and the denominator would give you $$\frac{cos(45)(601-148)}{cos(45)sin(21.8)}$$ and the cosines would cancel which is not what you want.

 

[Ryuk1990]

Ok, thanks guys.

 

[CellCoree]

In this expression, the cosine function is being applied to the entire fraction, not just the numerator. This means that the cosine function will be distributed to both the numerator and denominator. This is because the order of operations dictates that we first evaluate the expression within the parentheses, then apply the cosine function to the result. So in this case, the cosine function will be distributed to both the numerator (601-148) and the denominator (sin21.8). This is important to keep in mind when simplifying the expression further.

 

[pmacias]

In this expression, cos45 is being multiplied into both the numerator and the denominator. The distribution property in mathematics allows us to distribute a term to all the terms within a set of parentheses. Therefore, cos45 would be multiplied into both the 601 and 148 in the numerator, as well as the sin21.8 in the denominator. This is because cos45 is being multiplied by the entire expression within the parentheses.