

follows from the fact that the cosine function is

-periodic, which means

. Roughly speaking, this is the same as saying that a point on a circle is the same as the point you get by completing a full revolution around the circle (i.e. add

to the original point's angle with respect to the horizontal axis).
If you make another complete revolution (so we're effectively adding

) we get the same result:

. This is true for any number of complete revolutions, so that this pattern holds for any even multiple of

added to the argument. Therefore

for any integer

.
Next, because

, it follows that

is also true for any integer

. So we have

The rest follows from considering either case and solving for

.
I think the answer to this question is (C) $36.36.
Answer:
see explanation
Step-by-step explanation:
In 13 - 17
Consider the factors of the constant term which sum to give the coefficient of the x- term
13
x² - x - 42 = (x - 7)(x + 6)
15
x² + x - 6 = (x + 3)(x - 2)
17
x² - 27x + 50 = (x - 25)(x - 2)
19
r² - 25 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , thus
r² - 25
= r² - 5² = (r - 5)(r + 5)
1. 24
2.-40
3.-8a-8b
4. 10b+40
5. -2p-14
I believe these are right, hope this helps!!