maryamalraish
maryamalraish maryamalraish
  • 03-01-2018
  • Mathematics
contestada

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.

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wizard123
wizard123 wizard123
  • 03-01-2018
sub in given values to get 2 equations.

[tex]a + b \cos(2*0) = -1 \rightarrow a+b = -1 \\ \\ a+b \cos(2*\frac{\pi}{2}) = 7 \rightarrow a - b = 7[/tex]

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

Sub into first equation to get value for 'b'
[tex]3+b = -1 \\ \\ b = -4[/tex]
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