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UCE (O-Level) Trigonometric Functions — practice questions

Explore 3 free Trigonometric Functions questions in UCE (O-Level) 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 1–3 of 3.

A sailor in a boat looks up at the top of a cliff. What is the angle between the line of sight and the horizontal called?Read the answer and worked solution →An observer stands on top of a cliff and looks down at a boat below. What is the angle between the line of sight and the horizontal called?Read the answer and worked solution →Which result is used alongside the three trigonometric ratios to solve two-dimensional problems?Read the answer and worked solution →

Worked practice questions

A sailor in a boat looks up at the top of a cliff. What is the angle between the line of sight and the horizontal called?

  1. The angle of depression
  2. The angle of reflection
  3. The angle of rotation
  4. The angle of elevation
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Correct answer: D. The angle of elevation

1. The top of the cliff sits above the horizontal plane through the sailor's eyes. 2. The angle of elevation is the angle formed by the line of sight and the horizontal plane for an object above it. 3. The cliff can be treated as a vertical line, which gives a right-angled triangle. 4. In trigonometry the angle of inclination means the same thing as the angle of elevation. _Source: Siyavula Mathematics Grade 10 (Everything Maths, CC BY 4.0), Chapter 11: Trigonometry_

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An observer stands on top of a cliff and looks down at a boat below. What is the angle between the line of sight and the horizontal called?

  1. The angle of depression
  2. The angle of elevation
  3. The angle of incidence
  4. The angle of inclination
Show answer and solution

Correct answer: A. The angle of depression

1. The boat sits below the horizontal plane through the observer's eyes. 2. The angle of depression is the angle formed by the line of sight and the horizontal plane for an object below it. 3. The angle of elevation from the boat back up to the observer has the same size. 4. The angle of inclination is another name for the angle of elevation, so it names the upward case. _Source: Siyavula Mathematics Grade 10 (Everything Maths, CC BY 4.0), Chapter 11: Trigonometry_

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Which result is used alongside the three trigonometric ratios to solve two-dimensional problems?

  1. The mid-point theorem
  2. The theorem of Pythagoras
  3. The remainder theorem
  4. The factor theorem rule
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Correct answer: B. The theorem of Pythagoras

1. The three trigonometric ratios are sine, cosine and tangent. 2. Each ratio links one angle to two of the three sides of a right-angled triangle. 3. Sometimes a problem gives two sides and needs the third one before a ratio can be used. 4. The theorem of Pythagoras supplies that missing third side. 5. These three ratios and the theorem of Pythagoras together solve two-dimensional problems. 6. The mid-point theorem belongs to geometry of triangles and says nothing about angles in a right-angled triangle. _Source: Siyavula Mathematics Grade 10 (Everything Maths, CC BY 4.0), Chapter 11: Trigonometry_

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