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In die diagram is die grafieke van $f(x) = ext{sin} 2x$ en $h(x) = ext{cos}(x-45^{ ext{o}})$ vir die interval $x ext{ E } [-180^{ ext{o}}; 180^{ ext{o}}]$ - NSC Mathematics - Question 6 - 2017 - Paper 2
Question 6
![In-die-diagram-is-die-grafieke-van---$f(x)-=--ext{sin}-2x$-en-$h(x)-=--ext{cos}(x-45^{-ext{o}})$-vir-die-interval---$x--ext{-E-}-[-180^{-ext{o}};-180^{-ext{o}}]$-NSC Mathematics-Question 6-2017-Paper 2.png](https://cdn.simplestudy.cloud/assets/backend/uploads/question/subject_692_paper_20410_q6_679949c8.jpg)
In die diagram is die grafieke van $f(x) = ext{sin} 2x$ en $h(x) = ext{cos}(x-45^{ ext{o}})$ vir die interval $x ext{ E } [-180^{ ext{o}}; 180^{ ext{o}}]$. ... show full transcript
Worked Solution & Example Answer:In die diagram is die grafieke van $f(x) = ext{sin} 2x$ en $h(x) = ext{cos}(x-45^{ ext{o}})$ vir die interval $x ext{ E } [-180^{ ext{o}}; 180^{ ext{o}}]$ - NSC Mathematics - Question 6 - 2017 - Paper 2
Step 3
Gebruik die grafieke om $2 ext{sin} x ext{cos} x ext{≤} rac{1}{ ext{√}2} ext{sin} x$ vir die interval $x ext{ E } [-180^{ ext{o}}; 180^{ ext{o}}]$ op te los. Toon ALLE bewerkings.
Answer
Om die ongelykheid op te los:
egin{align*} ext{sin} 2x & ext{≤} rac{1}{ ext{√}2} ext{sin} x\ ext{sin} 2x & ext{≤} ext{cos} 45^{ ext{o}} ext{cos} x + ext{sin} 45^{ ext{o}} ext{sin} x\ ext{sin} 2x & ext{≤} ext{cos}(x - 45^{ ext{o}})\ x & ext{ E } [-75^{ ext{o}}; 165^{ ext{o}}]\ ext{cos}(x - 45^{ ext{o}}) & ext{≤} 0\ ext{Thus, the intervals we calculate will lead us to find the solutions.}\ ext{Answer: } x ext{ values for the solution are obtained from the inequality above.} ext{ Use graphical or tabular methods to find the exact intersections.} ext{ Values include certain ranges derived from } [-75^{ ext{o}}, 165^{ ext{o}}].