Verifying an Identity

Question

Hi!

I need some assistance answering these questions about the graph: What do you notice about the two graphs? Use your graph to come up with a relationship between the two expressions for the given functions.

Here are the functions both graphed: f(x)=sin⁡x, g(x)=cos⁡(x-π/2).

I have already put them on a graph and they are similar.

They lie on each other; almost as if they are similar functions and they have the same coordinates.

I just do not really know how to explain it more and how to come up with a relationship between both.

Thank you so much!

Answer 1

Following over from my colleague,

if you use the identity: sin^2(x) + cos^2(x) = 1:

we can see that when x= pi, sin(pi)= 0 while cos(pi)= -1, and when we square -1, we get +1. So they’re cofunctions of each other due to that identity.

Answer 2

f(x) = sinx

g(x) = cos(x-pi/2)

their relationship is they're identical

f(x)=g(x), not just f(x)=g(x), but f(x)=g(x), with 3 horiztal lines

sin(x) = cos(x-pi/2)

they're identical functions,

not just equal, but identical, for any and all values of x

the cosine of x = the sine of the angle complementary to x

and vice versa

the sine of x = the cosine of the angle complementary to x

It's why they're called "cofunctions." cosine is the cofunction of sine

same with tangent and cotangent or secant and cosecant