Use the image below to answer the following question. what relationship do the ratios of sin x and cos y share?
a. the ratios are opposites (-5/13 and 5/13)
b. the ratios are both indentical (5/13 and 5/13)
c. the ratios are reciprocals (5/13 and 13/5)
d. the ratios are both negative (-13/5 and -13/5)

Option B.

Step-by-step explanation:

we know that

In a right triangle

because

-----> complementary angles

Verify

The sine of angle x is equal to divide the opposite side angle x by the hypotenuse

The cosine of angle y is equal to divide the adjacent side to angle y by the hypotenuse

therefore

The ratios are both identical (5/13 and 5/13)

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1