Question

The maximum value of $5+(sinx-4{)}^2$ is

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Answer 1

Maximum value of 5 + $(sinx-4{)}^2$ is 5 + maximum value of $(sinx-4{)}^2$. So we want to find the maximum value of $(sinx-4{)}^2$

sin x varies from -1 to 1.|sinx - 4| is the distance of sinx from 4. This distance is maximum when sin x is -1 $(sinx-4{)}^2$ will be maximum when |sin x - 4| is maximum.This happens when sin x = -1

Maximum value = $5+(-1-4{)}^2=5+5^2=30$