gaokao 2022 Q6

gaokao · China · national-I Trig Graphs & Exact Values

6. Let the function $f ( x ) = \sin \left( \omega x + \frac { \pi } { 4 } \right) + b$ ( $\omega > 0$ ) have minimum positive period $T$. If $\frac { 2 \pi } { 3 } < T < \pi$ and the graph of $y = f ( x )$ is symmetric about the point $\left( \frac { 3 \pi } { 2 } , 2 \right)$, then $f \left( \frac { \pi } { 2 } \right) =$
A. $1$
B. $\frac { 3 } { 2 }$
C. $\frac { 5 } { 2 }$
D. $3$

Let the function $f ( x ) = \sin \left( \omega x + \frac { \pi } { 4 } \right) + b ( \omega > 0 )$ have minimum positive period $T$ . If $\frac { 2 } { 3 } \pi < T < \pi$ , and the graph of $y = f ( x )$ is centrally symmetric about the point $\left( \frac { 3 \pi } { 2 } , 2 \right)$ , then $f \left( \frac { \pi } { 2 } \right) =$

6. Let the function $f ( x ) = \sin \left( \omega x + \frac { \pi } { 4 } \right) + b$ ( $\omega > 0$ ) have minimum positive period $T$. If $\frac { 2 \pi } { 3 } < T < \pi$ and the graph of $y = f ( x )$ is symmetric about the point $\left( \frac { 3 \pi } { 2 } , 2 \right)$, then $f \left( \frac { \pi } { 2 } \right) =$\\
A. $1$\\
B. $\frac { 3 } { 2 }$\\
C. $\frac { 5 } { 2 }$\\
D. $3$

Paper Questions

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