Trigonometric functions and their graphsIB MYP Maths Extended: Mind map

Exam questions on Trigonometric functions and their graphs

1. A function is defined by $y=3\sin(2x)+1$ for $0^\circ\le x\le360^\circ$.
   Write down the equation of the midline of the graph and its amplitude.2 marks
2. A student uses technology to draw the graph of $y=\sin(bx)$ for $0^\circ\le x\le360^\circ$ and records the period for several values of $b$: $b=1$ gives $360^\circ$, $b=2$ gives $180^\circ$, $b=3$ gives $120^\circ$ and $b=4$ gives $90^\circ$.
   The student now graphs $y=\sin(bx)$ and finds that the period is $45^\circ$. Use the rule to find $b$, and verify your answer by checking that the rule still gives the recorded period when $b=4$.2 marks
3. The depth of water, $h$ metres, in a harbour in Lisbon is modelled by $h=2\sin(30t)+5$, where $t$ is the time in hours after midnight and $0\le t\le12$. The angle $30t$ is measured in degrees.
   State the greatest depth, the least depth and the time between two consecutive high tides.3 marks