Trigonometric Graphs

New Zealand

Level 7 - NCEA Level 2

Consider the given graph of $y=\cos\left(x+180^\circ\right)$`y`=`c``o``s`(`x`+180°).

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a

What is the amplitude of the function?

b

How can the graph of $y=\cos x$`y`=`c``o``s``x` be transformed into the graph of $y=\cos\left(x+180^\circ\right)$`y`=`c``o``s`(`x`+180°)?

By reflecting it about the $x$`x`-axis, and then translating it horizontally $180$180 units to the left.

A

By translating it horizontally $180$180 units to the right.

B

By translating it horizontally $180$180 units to the left.

C

By changing the period of the function.

D

By reflecting it about the $x$`x`-axis, and then translating it horizontally $180$180 units to the right.

E

Easy

Less than a minute

Consider the function $f\left(x\right)=\sin x$`f`(`x`)=`s``i``n``x` and $g\left(x\right)=\sin\left(x-90^\circ\right)$`g`(`x`)=`s``i``n`(`x`−90°).

Consider the function $f\left(x\right)=\cos x$`f`(`x`)=`c``o``s``x` and $g\left(x\right)=\cos\left(x-90^\circ\right)$`g`(`x`)=`c``o``s`(`x`−90°).

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

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