Grade 10 Maths · Trigonometry

Use cosec, sec and cot

Use cosec, sec and cot as the flipped versions of sin, cos and tan, for example if sin θ = 3/5 then cosec θ = 5/3.

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Grade 10 Trigonometry: Reciprocals of trig ratiosMiss Martins Maths and Science

Reciprocal Trig Ratios | Cosec, Sec and Cot | Grade 10 CAPS MathsBrainy X

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Question 4.2.2 · November 2024 · Paper 2 · Provincial · 3 marks

In the diagram is a right-angled triangle has sides a, b and c and the

\hat{B} = 9 0^{\circ}

4.2 Given:

13 cos θ = 12

, where

0^{\circ} \leq θ \leq 9 0^{\circ}

, without using a calculator, use a sketch to determine the following.

4.2.2

tan θ - cosec^{2} θ

(3)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: use cosec, sec and cot

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3. Question 2.1.2 · June 2024 · Paper 2 · Provincial · 2 marks
2.1 If $A = 7 8^{\circ}$ and $B = 3 4^{\circ}$ , calculate the values of the following expressions, correct to two decimal places.
2.1.2 $3 sec A$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Convert sec to cos $3 \frac{1}{c o s 7 8 ^{\circ}}$
  1 mark · Use cosec, sec and cot
2. ✓
  Calculate value $= 1, 69$
  1 mark · Use cosec, sec and cot
4. Question 3.1.3 · March 2023 · Provincial · 2 marks
In $Δ A BC$ , $\hat{C} = 9 0^{\circ}$ and $\hat{B} = θ$ , $A C = 7$ units, $BC = 5$ units and $A B = 74$ units.
3.1 Use the diagram above to write down the value of: (Leave your answer in surd form)
3.1.3 $cosec^{2} θ$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Substitute ratio $(\frac{74}{7})^{2}$
  1 mark · Use cosec, sec and cot
2. ✓
  Simplify $\frac{74}{49}$
  1 mark · Use cosec, sec and cot
5. Question 3.1.2 · March 2025 · Provincial · 3 marks
In $Δ PQR$ , $QR = 4 cm$ , $PR = 5 cm$ and $QP = 3 cm$ . $PQ$ is perpendicular to $QR$ and $\hat{P} = θ$ , $P \hat{R} Q = α$ .
3.1 Calculate the following ratios:
3.1.2 $sec α$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Recall definition of secant $sec α = \frac{1}{c o s α}$
  1 mark · Use cosec, sec and cot
2. ✓
  Substitute cosine ratio $cos α = \frac{QR}{PR} = \frac{4}{5}$
  $sec α = \frac{1}{\frac{4}{5}}$
  1 mark · Write trig ratios in a triangle
3. ✓
  Calculate final value $= \frac{5}{4}$
  1 mark · Use cosec, sec and cot
6. Question 4.1.2 · March 2023 · Provincial · 3 marks
4.1 Solve for x where $0^{\circ} \leq x \leq 9 0^{\circ}$ , in each of the following equations. Give your answer correct to TWO decimal places.
4.1.2 $cosec (x - 3 5^{\circ}) = 7, 814$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Write cosec as 1/sin $\frac{1}{s i n ( x - 3 5 ^{\circ} )} = 7, 814$
  1 mark · Use cosec, sec and cot
2. ✓
  Cross multiplication $sin (x - 3 5^{\circ}) = \frac{1}{7 , 814}$
  1 mark · Use cosec, sec and cot
3. ✓
  Answer $x - 3 5^{\circ} = 7, 3 5^{\circ}$
  $x = 42, 3 5^{\circ}$
  1 mark · Calculate an angle from a ratio

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