The function f(x)=asinx+b is defined for the domain 0<x<2pi.?

Question

given that f(pi/2)=2 and f(3pi/2)=-8. find the values of a and b.

Answer 1

sin(pi/2) = 1 then f(pi/2) = a + b = 2

sin(3pi/2) = -1 then f(3pi/2) = -a + b = -8

2b = 2 - 8 = - 6 then b = -3

a = 2 - b = 2 + 3 = 5

f(x) = 5sinx - 3

Answer 2

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