Die grafieke hieronder verteenwoordig die funksies gedefinieer deur $f(x) = ext{cos} heta$ en $g(x) = ext{tan} x$ vir $x ext{ in } [0^{ extcirc}; 180^{ extcirc}]$ - NSC Technical Mathematics - Question 5 - 2023 - Paper 2
Question 5
Die grafieke hieronder verteenwoordig die funksies gedefinieer deur $f(x) = ext{cos} heta$ en $g(x) = ext{tan} x$ vir $x ext{ in } [0^{ extcirc}; 180^{ extcirc}]... show full transcript
Worked Solution & Example Answer:Die grafieke hieronder verteenwoordig die funksies gedefinieer deur $f(x) = ext{cos} heta$ en $g(x) = ext{tan} x$ vir $x ext{ in } [0^{ extcirc}; 180^{ extcirc}]$ - NSC Technical Mathematics - Question 5 - 2023 - Paper 2
Step 1
Die waarde van $a$
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Answer
Die waarde van a in die grafiek is 1.
Step 2
Die periode van $g$
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Answer
Die periode van die tan-funksie is 180extcirc.
Step 3
Die waarde van $x$ waarvoor $ ext{tan} x + 1 = 0$
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Answer
Om exttanx+1=0 op te los, stel ons exttanx=−1. Die oplossing is x=135extcirc.
Step 4
Die waardeverzameling van $g$
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Die waardeverzameling van g is (- rac{ ext{onbounded}}{2}, rac{ ext{onbounded}}{2}).
Step 5
Die waarde(s) van $x$ waarvoor $f(x) < 0$
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Die waarde(s) van x waarvoor f(x)<0 is in die interval (90extcirc,180extcirc).
Step 6
Bepaal $g(180^{ extcirc}) - f(180^{ extcirc})$
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Gegee dat g(180extcirc)=exttan(180extcirc)=0 en f(180extcirc)=extcos(180extcirc)=−1, dan is:
![Die-grafieke-hieronder-verteenwoordig-die-funksies-gedefinieer-deur-$f(x)-=--ext{cos}--heta$-en-$g(x)-=--ext{tan}-x$-vir-$x--ext{-in-}-[0^{-extcirc};-180^{-extcirc}]$-NSC Technical Mathematics-Question 5-2023-Paper 2.png](https://cdn.simplestudy.io/assets/backend/uploads/question/subject_1520_paper_20921_q5_679a5deb.jpg)
