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NSC / Matric Trigonometric Functions — practice questions

Explore 2 free Trigonometric Functions questions in NSC / Matric Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Trigonometric Functions questions and exercises with answers

Showing questions 1–2 of 2.

Why does a trigonometric equation have infinitely many solutions unless the domain is restricted?Read the answer and worked solution →When solving a trigonometric equation, what is the CAST diagram used for?Read the answer and worked solution →

Worked practice questions

Why does a trigonometric equation have infinitely many solutions unless the domain is restricted?

  1. The functions are always positive
  2. The functions repeat periodically
  3. The functions have no maximum
  4. The functions are not continuous
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Correct answer: B. The functions repeat periodically

1. Sine, cosine and tangent all repeat their values after a fixed interval of angle. 2. So once one angle satisfies an equation, adding whole periods to it gives more angles that also satisfy it. 3. Subtracting whole periods works in the same way and gives negative angles. 4. That is why a general solution is written with a whole number of periods added on. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 4: Trigonometry_

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When solving a trigonometric equation, what is the CAST diagram used for?

  1. To find the size of the reference angle
  2. To find the period of the function
  3. To find where the ratio is positive
  4. To find the value of the amplitude
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Correct answer: C. To find where the ratio is positive

1. A calculator returns only one angle, called the reference angle, for a given ratio. 2. But the same ratio has the same sign in two of the four quadrants. 3. The CAST diagram records which trigonometric ratios are positive in each quadrant. 4. It is therefore used to decide which quadrants the solutions lie in. 5. The reference angle itself comes from the calculator, not from the diagram. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 4: Trigonometry_

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