Find the range of the given function f(x) = 3sin x + 8 cos(x - pi/3) +5 - Maths - Relations and Functions

Question

Find the range of the given function f(x) = 3sin x + 8 cos(x -
pi/3) +5

Rajat Sethi · Accepted Answer

f(x)=3sinx+8cos(x-π3)+5f(x)=3sinx+8[cosx cos(π3)+sinx
sin(π3)] + 5 [Using cos(A-B)=cosA
cosb +sinA
sinB]f(x)=3sinx+8cosx2+83sinx2+5f(x)=(3+43)sinx +4cosx +5We know,maximum and minimum values of asinx+bcosx+c are c+a2+b2and c-a2+b2 respectively
∴Maximum value of f(x) =5+(3+43)2+42=5+73+243Minimum value of f(x) =5-(3+43)2+42=5-73+243Range of f(x):5-73+243≤f(x)≤5+73+243