In the diagram below, the graph of $f(x) = -2 ext{sin} x$ is drawn for the interval $x orall [-180^{ ext{o}} ; 180^{ ext{o}}].$
7.1 On the grid provided in the ANSWER BOOK, draw the graph of $g(x) = ext{cos}(x - 60^{ ext{o}})$ for $x orall [-180^{ ext{o}} ; 180^{ ext{o}}]$ - NSC Mathematics - Question 7 - 2021 - Paper 2
Question 7
In the diagram below, the graph of $f(x) = -2 ext{sin} x$ is drawn for the interval $x orall [-180^{ ext{o}} ; 180^{ ext{o}}].$
7.1 On the grid provided in the ANS... show full transcript
Worked Solution & Example Answer:In the diagram below, the graph of $f(x) = -2 ext{sin} x$ is drawn for the interval $x orall [-180^{ ext{o}} ; 180^{ ext{o}}].$
7.1 On the grid provided in the ANSWER BOOK, draw the graph of $g(x) = ext{cos}(x - 60^{ ext{o}})$ for $x orall [-180^{ ext{o}} ; 180^{ ext{o}}]$ - NSC Mathematics - Question 7 - 2021 - Paper 2
Step 1
7.1 On the grid provided in the ANSWER BOOK, draw the graph of $g(x) = ext{cos}(x - 60^{ ext{o}})$ for $x orall [-180^{ ext{o}} ; 180^{ ext{o}}]$
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Answer
To draw the graph of g(x)=extcos(x−60exto):
Start by noting the amplitude, which is 1.
The phase shift is to the right by 60°.
Plot key points:
The function has a maximum at x=60exto.
The first x-intercept occurs at x=60exto+90exto=150exto.
The second x-intercept occurs at x=60exto−90exto=−30exto.
Draw the graph, ensuring to include both turning points and the specified x-intercepts.
Step 2
7.2 Write down the period of $f(3x)$
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Answer
The period of a sine function is calculated through the formula:
ext{Period} = rac{360^{ ext{o}}}{|B|}
where B is the coefficient of x in f(x)=−2extsin(3x).
In this case, B=3, thus the period of f(3x) is:
ext{Period} = rac{360^{ ext{o}}}{3} = 120^{ ext{o}}
Step 3
7.3 Use the graphs to determine the value of $x$, if $x orall [-180^{ ext{o}} ; 180^{ ext{o}}]$ for which $f(x) = g(x) = 1$
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Answer
From the graphs:
f(x) reaches its maximum value of 1 at x=−90exto.
g(x) achieves its maximum value of 1 at x=150exto.
Hence, we find:
x=−30exto
Step 4
7.4 Write down the range of $k$, if $k(x) = rac{1}{2} g(x) + 1$
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Answer
For g(x), the function varies between -1 and 1 over the specified interval:
![In-the-diagram-below,-the-graph-of-$f(x)-=--2-ext{sin}-x$-is-drawn-for-the-interval-$x--orall-[-180^{-ext{o}}-;-180^{-ext{o}}].$--7.1-On-the-grid-provided-in-the-ANSWER-BOOK,-draw-the-graph-of-$g(x)-=--ext{cos}(x---60^{-ext{o}})$-for-$x--orall-[-180^{-ext{o}}-;-180^{-ext{o}}]$-NSC Mathematics-Question 7-2021-Paper 2.png](https://cdn.simplestudy.io/assets/backend/uploads/question/subject_692_paper_20442_q7_679949c8.jpg)
