Explain why you cannot use the Distributive Property to evaluate an expression in the form of sin(a + b). Please illustrate with an example along with your explanation.

The distributive property is to multiply the outside of a parenthesis by each term inside, for example:

this cannot be done with the trigonometric functions such as the sine.

An example of this:

let's prove that we don't get the correct result using the distributive property in the following expression:

≠

We add the elements in the parentheses on the left side:

 ≠

this are known values of the sine function:

substituting these values we will get that:

-1  ≠ 0 +1

-1  ≠ 1

Thus we notice that we don't get the correct result using the distributive property.

The correct way to express the angle sum in the sine function is:

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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