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Trigonometry

Trigonometry

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Why this why now

Pupils have recently learned about geometrical properties of similarity and the Pythagorean Theorem. This knowledge is further developed to build on their understanding of congruence and similarity with right-angled triangles. In this unit, similarity is used to extend a right-angled triangle in the unit circle to any other right-angled triangle.

Prior knowledge requirements

  • Label sides in right-angled triangles (opposite, adjacent, hypotenuse)
  • Use sine, cosine and tangent ratios
  • Rearrange and solve trigonometric equations

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Why this why now

Pupils have recently learned about geometrical properties of similarity and the Pythagorean Theorem. This knowledge is further developed to build on their understanding of congruence and similarity with right-angled triangles. In this unit, similarity is used to extend a right-angled triangle in the unit circle to any other right-angled triangle.

Prior knowledge requirements

  • Label sides in right-angled triangles (opposite, adjacent, hypotenuse)
  • Use sine, cosine and tangent ratios
  • Rearrange and solve trigonometric equations

Trigonometry

In this unit pupils learn how to recognise the relationship between the unit circle and the trigonometric ratios of sine, cosine and tangent. Pupils then apply this knowledge to solve trigonometric problems.

12 lessons in unit

  1. 1

    Checking and securing understanding of similar triangles

    I can recognise that similar shapes have sides in proportion to each other but angle sizes are preserved.
  2. 2

    Checking and securing understanding of Pythagoras' theorem

    I can use Pythagoras' theorem to find the length of any side of a right-angled triangle.
  3. 3

    The unit circle

    I can appreciate that the trigonometric functions are derived from measurements within a unit circle.
  4. 4

    Scaling the right-angled triangle from the unit circle

    I can recognise the right-angled triangle within a unit circle and use proportion to scale to similar triangles.
  5. 5

    Sine and cosine ratios

    I can derive the sine and cosine ratios from the sides of a right-angled triangle.
  6. 6

    Tangent ratio

    I can derive the tangent ratio from the sides of a right-angled triangle.
  7. 7

    Using the sine ratio

    I can use the sine ratio to find the missing side or angle in a right-angled triangle.
  8. 8

    Using the cosine ratio

    I can use the cosine ratio to find the missing side or angle in a right-angled triangle.
  9. 9

    Using the tangent ratio

    I can use the tangent ratio to find the missing side or angle in a right-angled triangle.
  10. 10

    Choosing the right trigonometric ratio

    I can choose the appropriate trigonometric ratio to use to solve problems in right-angled triangles.
  11. 11

    Choosing an appropriate method for finding lengths of a triangle

    I can choose the appropriate method to find the missing side in a right-angled triangle.
  12. 12

    Problem solving with trigonometry

    I can use my knowledge of trigonometry to solve problems.

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