NSC Technical Mathematics Trigonometry: Gegee: ˆA = 66° en ˆB = 59° Bep

Gegee: ˆA = 66° en ˆB = 59° Bepaal die waarde van: 3.1.1 sin B 3.1.2 sec A + cos B Gegee: tan α = - 2/3 en α ∈ [180°, 360°] Bepaal, met behulp van 'n diagram en sonder die gebruik van 'n sakrekenaar, die waarde van 4cot α + sin α Los op vir x: cosecx = -3,054 en x ∈ [0°; 360°] - NSC Technical Mathematics - Question 3 - 2023 - Paper 2

Question 3

Gegee:-ˆA-=-66°-en-ˆB-=-59°--Bepaal-die-waarde-van:--3.1.1-sin-B--3.1.2-sec-A-+-cos-B--Gegee:-tan-α-=---2/3-en-α-∈-[180°,-360°]--Bepaal,-met-behulp-van-'n-diagram-en-sonder-die-gebruik-van-'n-sakrekenaar,-die-waarde-van-4cot-α-+-sin-α--Los-op-vir-x:--cosecx-=--3,054-en-x-∈-[0°;-360°]-NSC Technical Mathematics-Question 3-2023-Paper 2.png

Gegee: ˆA = 66° en ˆB = 59° Bepaal die waarde van: 3.1.1 sin B 3.1.2 sec A + cos B Gegee: tan α = - 2/3 en α ∈ [180°, 360°] Bepaal, met behulp van 'n diagram en... show full transcript

Worked Solution & Example Answer:Gegee: ˆA = 66° en ˆB = 59° Bepaal die waarde van: 3.1.1 sin B 3.1.2 sec A + cos B Gegee: tan α = - 2/3 en α ∈ [180°, 360°] Bepaal, met behulp van 'n diagram en sonder die gebruik van 'n sakrekenaar, die waarde van 4cot α + sin α Los op vir x: cosecx = -3,054 en x ∈ [0°; 360°] - NSC Technical Mathematics - Question 3 - 2023 - Paper 2

Step 1

3.1.1 sin B

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Answer

To determine the value of

ext{sin} B = ext{sin}(59°)

which evaluates approximately to 0.86.

Step 2

3.1.2 sec A + cos B

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Answer

To find the value of

ext{sec} A + ext{cos} B = ext{sec}(66°) + ext{cos}(59°)

First, note that

ext{sec} A = rac{1}{ ext{cos} A}

Thus,

ext{sec}(66°) = rac{1}{ ext{cos}(66°)} + ext{cos}(59°) \ = rac{1}{0.4067} + 0.5150 \ ≈ 2.97

Step 3

3.2 tan α = -2/3 en α ∈ [180°; 360°]

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Answer

We know that

an(α) = rac{ ext{opposite}}{ ext{adjacent}} \ in this case, opposite = -2 ext{ and adjacent} = 3 \ herefore r^2 = (-2)^2 + (3)^2 = 4 + 9 = 13 \ ext{so} \ r = ext{sqrt}(13)

Next, we calculate:

ext{cot} α = rac{1}{ an α} = rac{3}{2} \ herefore 4 ext{cot α} + ext{sin} α = 4 imes rac{3}{2} + ext{sin}(α)

Finally, we simplify the expression appropriately to solve.

Step 4

3.3 Los op vir x: cosecx = -3,054

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Answer

Starting with

ext{cosec}(x) = -3.054 \ ext{This means} \ ext{sin}(x) = rac{1}{-3.054} \ ≈ -0.327

We will consider the reference angle:

ext{Ref}(x) = 9.11° or x = 180° + 9.11° or 360° - 9.11° \ herefore x = 199.11° or x = 340.89°

3.1.1 sin B

3.1.2 sec A + cos B

3.2 tan α = -2/3 en α ∈ [180°; 360°]

3.3 Los op vir x: cosecx = -3,054

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