Question

The function f is defined by f(x) = a + bcos2x, for 0 ≤ x ≤ π. It is given that f(0)=−1 and f(1/2π) = 7. (i) Find the values of a and b.

Answer 1

Sub in given values to get 2 equations.

$a + b \cos(2*0) = -1 \rightarrow a+b = -1 \\ \\ a+b \cos(2*\frac{\pi}{2}) = 7 \rightarrow a - b = 7$

Solve system using elimination.  Add the equations together, cancelling out 'b'
$2a = 6 \\ \\ a = 3$

Sub into first equation to get value for 'b'
$3+b = -1 \\ \\ b = -4$