Question

Can someone please work this out for me I am not understanding it.
If 𝑓(𝑥) = cos 𝜋𝑥, find the exact value of a such that 𝑓(1)−𝑓(−1)/1-(-1)= cos a.

Answer 1

Plug in x = 1 to get
\[\Large f(x) = \cos(\pi*x)\]
\[\Large f(1) = \cos(\pi*1)\]
\[\Large f(1) = \cos(\pi)\]
\[\Large f(1) = -1\]
You'll use the unit circle
https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/2000px-Unit_circle_angles_color.svg.png
to compute the last part.

What do you get when you plug in x = -1 ?

Answer 2

\[\frac{ \cos \pi-\cos (-\pi) }{ 1-(-1) }=\frac{ \cos \pi-\cos \pi }{ 2 }=0=\cos a\]
\[\cos a=0=\cos \left( 2n +1 \right)\frac{ \pi }{ 2 },\]
where n is an integer.

Answer 3

\[\cos (-x)=\cos x\]

Answer 4

a=?