In die diagram hieronder is die grafiek van
f(x) = tan(x - 45°)
geset vir
x ∈ [-90°; 180°] - NSC Mathematics - Question 6 - 2023 - Paper 2
Question 6
In die diagram hieronder is die grafiek van
f(x) = tan(x - 45°)
geset vir
x ∈ [-90°; 180°].
6.1 Skryf die periode van f neer.
6.2 Op die rooster wat in die A... show full transcript
Worked Solution & Example Answer:In die diagram hieronder is die grafiek van
f(x) = tan(x - 45°)
geset vir
x ∈ [-90°; 180°] - NSC Mathematics - Question 6 - 2023 - Paper 2
Step 1
Skryf die periode van f neer.
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Die periode van die funksie f(x) = tan(x - 45°) is 180°.
Step 2
Op die rooster wat in die ANTWOOORDEBOEK verskaf word, skets die grafiek van g(g) = -cos 2x vir die interval x ∈ [-90°; 180°].
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Die grafiek van g(x) = -cos 2x is 'n kromme wat begin op g(-90°) = 1, met x-afsnitte by -45° en 0°, en eindig op g(180°) = -1. Die maksimum punte is by -90° en 90°, terwyl die minimum punt by 135° voorkom.
Step 3
Skryf die waardeversameling van g neer.
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Die waardeversameling van g is y ∈ [-1; 1].
Step 4
Die grafiek van g word 45° na links geskuif om die grafiek van h te vorm. Bepaal die vergelyking van h in sy eenvoudigste vorm.
98%
120 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Na die 45° skuif is die nuwe vergelyking h(x) = -cos(2(x + 45°)) = -cos(2x + 90°) = sin(2x).
Step 5
Gebruik die grafiek(e) om die waardes van x in die interval x ∈ [-90°; 90°], te bepaal waarvoor.
97%
117 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
6.5.1 Die onregte gelykheid f(x) > 1 is waar wanneer x < -30° of x > 30°.
6.5.2 Die onregte gelykheid 2 cos 2x - 1 > 0 is waar wanneer cos 2x > 1/2, wat lei tot die oplossing x ∈ (-30°; 30°).
![In-die-diagram-hieronder-is-die-grafiek-van---f(x)-=-tan(x---45°)---geset-vir---x-∈-[-90°;-180°]-NSC Mathematics-Question 6-2023-Paper 2.png](https://cdn.simplestudy.cloud/assets/backend/uploads/question/subject_692_paper_20453_q6_679949c8.jpg)
