Trig Functions and Graphs (radians)

Hong Kong

Stage 4 - Stage 5

The functions $f\left(x\right)$`f`(`x`) and $g\left(x\right)=f\left(x-k\right)-j$`g`(`x`)=`f`(`x`−`k`)−`j` have been graphed on the same set of axes in grey and black respectively.

Loading Graph...

a

What transformations have occurred from $f\left(x\right)$`f`(`x`) to $g\left(x\right)$`g`(`x`)?

Select all that apply.

Horizontal translation of $\frac{\pi}{3}$π3 radians right.

A

Vertical translation of $\frac{\pi}{3}$π3 units up.

B

Vertical translation of $3$3 units down.

C

Horizontal translation of $3$3 radians left.

D

b

Determine the value of $j$`j`.

c

Determine the smallest positive value of $k$`k`.

Easy

2min

The graph of $y=\cos x$`y`=`c``o``s``x` has been transformed into the graph of $y=\cos\left(2x+\frac{\pi}{3}\right)$`y`=`c``o``s`(2`x`+π3).

Easy

6min

Consider the graphs of $y=\sin x$`y`=`s``i``n``x` and $y=5\sin\left(x+\frac{\pi}{4}\right)$`y`=5`s``i``n`(`x`+π4).

Easy

1min

Consider the graphs of $y=\cos x$`y`=`c``o``s``x` and $y=3\cos\left(x-\frac{\pi}{4}\right)$`y`=3`c``o``s`(`x`−π4).

Easy

1min

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