Trigonometric Graphs

NZ Level 8 (NZC) Level 3 (NCEA) [In development]

Transformations of cot, sec and cosec curves and equations

Consider the graph of $y=\csc x$`y`=`c``s``c``x`. Its first local minimum for $x\ge0$`x`≥0 is at $\left(\frac{\pi}{2},1\right)$(π2,1).

By considering the transformation that has taken place, state the coordinates of the first local minimum of each of the given functions for $x\ge0$`x`≥0.

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a

$y=5\csc x$`y`=5`c``s``c``x`

b

$y=-5\csc x$`y`=−5`c``s``c``x`

c

$y=\csc x+2$`y`=`c``s``c``x`+2

Easy

Approx 4 minutes

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Display and interpret the graphs of functions with the graphs of their inverse and/or reciprocal functions