MathsYears 9–11Geometry - Properties of Shapes

Trigonometry: sin, cos and tan

Learn Trigonometry: sin, cos and tan for Years 9–11 pupils (ages 13–16). Free practice questions, lessons and worked examples — aligned to the UK National Curriculum.

What you'll learn

  1. 1

    In a right-angled triangle: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.

  2. 2

    The hypotenuse is always the longest side, opposite the right angle. Opposite and adjacent depend on which angle you are using.

  3. 3

    Which ratio uses opposite and adjacent?

  4. 4

    These ratios only work in RIGHT-ANGLED triangles. Without a right angle you need the sine or cosine rule instead.

  5. 5

    A right-angled triangle has hypotenuse 10 cm and an angle of 30°. The opposite side = 10 × sin(30°) = 10 × 0.5 = 5 cm.

  6. 6

    To find the opposite side given the hypotenuse and an angle, which ratio?

  7. 7

    When can you use Pythagoras instead of trigonometry?

Practise Trigonometry: sin, cos and tan with Whizlo

Free AI-tutored lessons, unlimited practice questions, and progress tracking for ages 13–16. Aligned to the UK National Curriculum.