Trigonometric functions and their graphsIB MYP Maths Extended: Flashcards

What these 13 flashcards ask

Period of y=\sin x and y=\cos x?
Period of y=\tan x?
Where are the asymptotes of y=\tan x for 0^\circ\le x\le360^\circ?
Range of values of y=\sin x?
Amplitude of y=a\sin(bx)+c?
Period of y=a\sin(bx)+c?
Midline of y=a\sin(bx)+c?
How do you find the amplitude from the greatest and least values?
Greatest and least values of y=3\sin(2x)+1?
Solutions of \sin x=0.5 for 0^\circ\le x\le360^\circ?
Solutions of \cos x=0.5 for 0^\circ\le x\le360^\circ?
Solutions of \tan x=1 for 0^\circ\le x\le360^\circ?
What does a negative a do to the graph of y=a\sin x?

Exam questions on Trigonometric functions and their graphs

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
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).