In die diagram is P(-5 ; 12) en T lê op die positiewe x-as - NSC Mathematics - Question 6 - 2020 - Paper 2
Question 6
In die diagram is P(-5 ; 12) en T lê op die positiewe x-as. PŌT = θ.
Beantwoord die volgende vrae sonder om 'n sakrekenaar te gebruik.
6.1.1 Skryf die waarde van t... show full transcript
Worked Solution & Example Answer:In die diagram is P(-5 ; 12) en T lê op die positiewe x-as - NSC Mathematics - Question 6 - 2020 - Paper 2
Step 1
6.1.1 Skryf die waarde van tan(θ) neer.
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Answer
Given the coordinates of point P(-5, 12), we can calculate the value of tan(θ) using the formula:
tan(θ)=adjacentopposite=−512=−512
Thus, the value of tan(θ) is (tan(θ) = -\frac{12}{5}).
Step 2
6.1.2 Bereken die waarde van cos(θ).
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Answer
To calculate cos(θ), we use the Pythagorean theorem to find the hypotenuse (OP):
OP=(−5)2+122=25+144=169=13
Now, using the definition of cosine:
cos(θ)=hypotenuseadjacent=13−5
So, the value of cos(θ) is (cos(θ) = -\frac{5}{13}).
Step 3
6.1.3 S(a ; b) is 'n punt in die derde kwadrant sodat TŌS = 0 + 90°. Bepaal die waarde van b.
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Answer
In the third quadrant, both sine and cosine are negative. Given TŌS = 0 + 90°, we know:
cos(90°+θ)=−sin(θ)
Using the cosine identity:
cos(θ)=6.5a
We have 5 as a known adjacent value, leading to:
b=(6.5)2−(5)2=42.25−25=17.25=−6.5b
Thus, the value of b will be derived accordingly.
