The relationship between the cosine and sine graphs is that the cosine is the same as the sine — only it’s shifted to the left by 90 degrees, or π/2. The trigonometry equation that represents this relationship is: cosx= sin (x+π/2)
The graphs of the sine and cosine functions illustrate a property that exists for several pairings of the different trig functions. The property represented here is based on the right triangle and the two acute or complementary angles in a right triangle. The identities that arise from the triangle are called the cofunctionidentities.
Answer:
The numbers are either {-3, -2, -1} or {7, 8, 9}.
Step-by-step explanation:
Let the smallest integer be represented by x. The middle number is x+1, and the largest number is x+2.
The product of the smaller and larger number is (x)(x+2).
15 more than 6 times the middle number is 6(x+1)+15.
(x)(x+2)=6(x+1)+15
x^2+2x=6x+6+15
x^2+2x=6x+21
x^2-4x-21=0
(x-7)(x+3)=0
x=-3 or x=7
The numbers are either {-3, -2, -1} or {7, 8, 9}.
Check the picture below, so pretty much reaches its maximum height at the vertex, now let's take a peek at the equation above hmmmm
![~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ h(t)=-16(t ~~ - ~~ \stackrel{h}{5})^2~~ + ~~\stackrel{k}{116}~\hfill \underset{maximum~height}{\stackrel{vertex}{(5~~,~~\underset{\uparrow }{116})}}](https://tex.z-dn.net/?f=~~~~~~%5Ctextit%7Bvertical%20parabola%20vertex%20form%7D%20%5C%5C%5C%5C%20y%3Da%28x-%20h%29%5E2%2B%20k%5Cqquad%20%5Cbegin%7Bcases%7D%20%5Cstackrel%7Bvertex%7D%7B%28h%2Ck%29%7D%5C%5C%5C%5C%20%5Cstackrel%7B%22a%22~is~negative%7D%7Bop%20ens~%5Ccap%7D%5Cqquad%20%5Cstackrel%7B%22a%22~is~positive%7D%7Bop%20ens~%5Ccup%7D%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20h%28t%29%3D-16%28t%20~~%20-%20~~%20%5Cstackrel%7Bh%7D%7B5%7D%29%5E2~~%20%2B%20~~%5Cstackrel%7Bk%7D%7B116%7D~%5Chfill%20%5Cunderset%7Bmaximum~height%7D%7B%5Cstackrel%7Bvertex%7D%7B%285~~%2C~~%5Cunderset%7B%5Cuparrow%20%7D%7B116%7D%29%7D%7D)
Answer: A: (6, 5)
Step-by-step explanation:
When graphing a system of equations, you can find the solution by finding where the graphs intersect. In this case, the graphs intersect at (6, 5).
To verify that this is indeed a solution to the system of equations, we can substitute (6, 5) into both of the given equations:
Since both equations hold true when plugging in the given coordinate (6, 5), we know that this is a solution to the system of equations.
