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Trigonometry: trigonometric ratios (sine, cosine, tangent) — KCSE Mathematics

KCSE Mathematics · 123 practice questions · 4 syllabus objectives

41 easy41 medium41 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Define sine, cosine and tangent of an acute angle in terms of sides of a right-angled triangle (SOH-CAH-TOA)

Use trigonometric tables or a calculator to find the values of sin, cos and tan for any angle from 0° to 360°

Apply trigonometric ratios to calculate unknown sides and angles in right-angled triangles in practical contexts

Trigonometry: trigonometric ratios (sine, cosine, tangent)

Sample Questions

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1
easySHORT ANSWER3 marks

A ladder leans against a wall, forming an angle of 60° with the ground. If the foot of the ladder is 2 m from the wall, find the length of the ladder. (3 marks)

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Part (a) — 3 marks
Uses cos(60°) = adjacent/hypotenuse (1 mk)
Substitutes values: cos(60°) = 2/Ladder length (1 mk)
Calculates Ladder length = 2/cos(60°) = 4 m (1 mk)
2
easySHORT ANSWER2 marks

In a right-angled triangle, the angle of elevation to the top of a hill from a point 30 m away from its base is 45°. Calculate the height of the hill. (2 marks)

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Part (a) — 2 marks
Recognises that tan(45°) = 1, thus height = distance from base (1 mk)
Height of the hill = 30 m (1 mk)
3
easySHORT ANSWER4 marks

Name the value of tan 60° without using a calculator. (4 marks)

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Part (a) — 4 marks
Correctly states tan 60° = √3 (1 mk)
Identifies decimal equivalent as approximately 1.732 (1 mk)
Mentions approximation to 2 decimal places as 1.73 (1 mk)
Explains that tan 60° is derived from the opposite and adjacent sides of a 30-60-90 triangle (1 mk)
4

Name the value of cos 45° using trigonometric tables. (3 marks)

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