Review question

# When does this trig function have its maximum value? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8411

## Solution

The greatest value which the function $f(x)=(3\sin^2(10x+11)-7)^2$ takes, as $x$ varies over all real values, equals

1. $-9$,
2. $16$,
3. $49$,
4. $100$.

We know that $\sin(10x+11)$ takes values between $-1$ and $1$.

So $\sin^2(10x+11)$ takes values between $0$ and $1$

So $3\sin^2(10x+11)$ takes values between $0$ and $3$

So $3\sin^2(10x+11)-7$ takes values between $-7$ and $-4$

So $f(x)$ takes values between $49$ and $16$, and the greatest value which $f(x)$ takes is $49$.