If 𝑓(𝑥) = cos 𝜋𝑥, find the exact value of a such that 𝑓(−1)−𝑓(1) /−1−1 = cos 𝑎.

Answer 1

f(-1) = cos -pi = cos pi = -1

f(1) = cos pi = -1

-1 - -1/-1 - 1 = cos A

-1 - 1 - 1 = cos A <--- division takes priority over subtraction!!! USE PARENTHESIS!!!

-3 = cos A

Since the cosine function is ALWAYS between -1 and +1, there is no solution for A.

Using parenthesis in the numerator but not the denominator

(-1 - -1)/-1 - 1 = sin A

0/-1 - 1 = sin A

0 - 1 = sin A

-1= sin A

A = pi + 2*n*pi where n is an integer

Using parenthesis in the numerator AND the denomiantor:

(-1 - -1) / (-1 - 1) = sin A

0 / -2 = sin A

0 = sin A

A = N/2*pi where n is an integer

so , as you can see, depending on the parenthesis, you get THREE different answers.

Which means YOU must figure out which one you need.