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Parents Pricing Home NSC Mathematics Functions In the diagram are the graphs of $f(x) = ext{sin } 2x$ and $h(x) = ext{cos }(x - 45^{ ext{o}})$ for the interval $x ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } x ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } [-180^{ ext{o}} ; 180^{ ext{o}}]$
In the diagram are the graphs of $f(x) = ext{sin } 2x$ and $h(x) = ext{cos }(x - 45^{ ext{o}})$ for the interval $x ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } x ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } [-180^{ ext{o}} ; 180^{ ext{o}}]$ - NSC Mathematics - Question 6 - 2017 - Paper 2 Question 6
View full question In the diagram are the graphs of $f(x) = ext{sin } 2x$ and $h(x) = ext{cos }(x - 45^{ ext{o}})$ for the interval $x ext{ } ext{ } ext{ } ext{ } ext{ } ext{ }... show full transcript
View marking scheme Worked Solution & Example Answer:In the diagram are the graphs of $f(x) = ext{sin } 2x$ and $h(x) = ext{cos }(x - 45^{ ext{o}})$ for the interval $x ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } x ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } [-180^{ ext{o}} ; 180^{ ext{o}}]$ - NSC Mathematics - Question 6 - 2017 - Paper 2
Write down the period of $f$. Only available for registered users.
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The period of the function f ( x ) = e x t s i n 2 x f(x) = ext{sin } 2x f ( x ) = e x t s in 2 x
ext{Period} = rac{360^{ ext{o}}}{n}
where n n n x x x f f f
ext{Period} = rac{360^{ ext{o}}}{2} = 180^{ ext{o}}
Determine the x-coordinate of B. Only available for registered users.
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The x-coordinate of point B can be found by identifying the intersection points of the graphs f f f h h h − 7 5 e x t o -75^{ ext{o}} − 7 5 e x t o
Use the graphs to solve $2 ext{sin } 2x ext{ } ext{ } ext{ } ext{ } rac{1}{ ext{$ ext{ } ext{ } ext{ } ext{ } ext{ }$} ext{$ ext{ } ext{ } ext{ } ext{ } ext{ }$} ext{ }} ext{cos }x + ext{sin }x$ for the interval $x ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ }[-180^{ ext{o}} ; 180^{ ext{o}}]$. Only available for registered users.
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To solve the equation, we first rewrite it as:
ext{sin } 2x ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } rac{1}{ ext{$ ext{ } ext{ } ext{ } ext{ } ext{ }$} ext{$ ext{ } ext{ } ext{ } ext{ } ext{ }$} ext{ }} ( ext{cos }x + ext{sin }x)
Next, substituting known values and solving gives:
e x t s i n 2 x e x t e x t e x t e x t e x t e x t e x t e x t e x t e x t e x t e x t e x t e x t e x t e x t e x t e x t e x t x e x t e x t e x t e x t e x t e x t e x t [ − 7 5 e x t o ; 16 5 e x t o ] . ext{sin } 2x ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } x ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } [-75^{ ext{o}} ; 165^{ ext{o}}]. e x t s in 2 x e x t e x t e x t e x t e x t e x t e x t e x t e x t e x t e x t e x t e x t e x t e x t e x t e x t e x t e x t x e x t e x t e x t e x t e x t e x t e x t [ − 7 5 e x t o ; 16 5 e x t o ] .
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![In-the-diagram-are-the-graphs-of-$f(x)-=--ext{sin-}-2x$-and-$h(x)-=--ext{cos-}(x---45^{-ext{o}})$-for-the-interval-$x--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}-x--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}--ext{-}-[-180^{-ext{o}}-;-180^{-ext{o}}]$-NSC Mathematics-Question 6-2017-Paper 2.png](https://cdn.simplestudy.io/assets/backend/uploads/question/subject_692_paper_20411_q6_679949c8.jpg)
