Trigonometric Graphs

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

Symmetrical and periodic nature of trig functions

Examine the graph of $y=\sin x$`y`=`s``i``n``x`.

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a

How long is one cycle of the graph?

b

State the $x$`x` values for which $\sin x=0$`s``i``n``x`=0, from $x=0$`x`=0 to $x=2\pi$`x`=2π inclusive.

c

State the first $x$`x` value for which $\sin x=0.5$`s``i``n``x`=0.5

d

Using the symmetry of the graph, for what other value of $x$`x` shown on the graph does $\sin x=0.5$`s``i``n``x`=0.5?

e

Using the symmetry of the graph, for what values of $x$`x` does $\sin x=-0.5$`s``i``n``x`=−0.5?

Easy

Approx 6 minutes

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