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Gegee: $x = 152,4^{ ext{o}}$ en $y = 24,8^{ ext{o}}$ Bepaal die volgende: 3.1.1 $sin(x - y)$ 3.1.2 $\frac{1}{2} sec\left(\frac{x}{2} + 80^{\text{o}}\right)$ - NSC Technical Mathematics - Question 3 - 2023 - Paper 2

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Gegee:-$x-=-152,4^{-ext{o}}$-en-$y-=-24,8^{-ext{o}}$--Bepaal-die-volgende:--3.1.1--$sin(x---y)$--3.1.2--$\frac{1}{2}-sec\left(\frac{x}{2}-+-80^{\text{o}}\right)$-NSC Technical Mathematics-Question 3-2023-Paper 2.png

Gegee: $x = 152,4^{ ext{o}}$ en $y = 24,8^{ ext{o}}$ Bepaal die volgende: 3.1.1 $sin(x - y)$ 3.1.2 $\frac{1}{2} sec\left(\frac{x}{2} + 80^{\text{o}}\right)$

Worked Solution & Example Answer:Gegee: $x = 152,4^{ ext{o}}$ en $y = 24,8^{ ext{o}}$ Bepaal die volgende: 3.1.1 $sin(x - y)$ 3.1.2 $\frac{1}{2} sec\left(\frac{x}{2} + 80^{\text{o}}\right)$ - NSC Technical Mathematics - Question 3 - 2023 - Paper 2

Step 1

3.1.1 $sin(x - y)$

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Answer

To find sin(xy)sin(x - y), we first calculate:

xy=152,4o24,8o=127,6ox - y = 152,4^{\text{o}} - 24,8^{\text{o}} = 127,6^{\text{o}}

Next, we compute:

sin(127,6o)0,8sin(127,6^{\text{o}}) \approx 0,8

Therefore, the answer is approximately 0,80,8.

Step 2

3.1.2 $\frac{1}{2} sec\left(\frac{x}{2} + 80^{\text{o}}\right)$

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Answer

First, we find x2\frac{x}{2}:

152,4o2=76,2o\frac{152,4^{\text{o}}}{2} = 76,2^{\text{o}}

Next, we evaluate:

x2+80o=76,2o+80o=156,2o\frac{x}{2} + 80^{\text{o}} = 76,2^{\text{o}} + 80^{\text{o}} = 156,2^{\text{o}}

Now we compute:

sec(156,2o)=1cos(156,2o)sec(156,2^{\text{o}}) = \frac{1}{cos(156,2^{\text{o}})}

Finally, the whole expression is:

12sec(156,2o)122,972,97\frac{1}{2} sec(156,2^{\text{o}}) \approx \frac{1}{2} \cdot 2,97 \approx 2,97

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