Question

if the greatest and smallest value of the function f(x)=a+b sin x is 7 and 1,then f(π/6)=?

Answer 1

check the attachment

Answer 2

Answer:

Step-by-step explanation:The greatest value sinx can take is 1 for π/2 and smallest value is -1 for -π/2.

f(π/2)=a+bsin(π/2)=7

a+b=7. ,......1

f(-π/2)=a+bsin(-π/2)=1

a-b=1. .......2

Solving eqns. 1 and 2, we get

a=4 and b=3

Therefore,

f(π/6)=a+bsin(π/6)=4+3/2=11/2