Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions.

Enlargement is a transformation that causes a change of size.

Scale factor is the multiplier between similar shapes that describes how large one shape is compared to the other.

Checking and securing understanding of similar triangles

Maths

Checking and securing understanding of Pythagoras' theorem

The unit circle

Scaling the right-angled triangle from the unit circle

Sine and cosine ratios

Tangent ratio

Using the sine ratio

Using the cosine ratio

Using the tangent ratio

Choosing the right trigonometric ratio

Choosing an appropriate method for finding lengths of a triangle

Problem solving with trigonometry

In this unit, pupils were introduced to the trigonometric ratios and developed the skills to ascertain which ratio would be appropriate for a given problem. In the future unit, pupils are introduced to a variety of situations where this knowledge is required, such as 3-D problems and elevation/depression.

In the prior unit, pupils continued 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.

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.

Trigonometry

The hypotenuse is the side of a right-angled triangle which is opposite the right angle.

Pythagoras’ theorem states that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse.

Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle for a given angle.

The sine of an angle (sin(θ°)) is the y-coordinate of point P on the triangle formed inside the unit circle.

The cosine of an angle (cos(θ°)) is the x-coordinate of point P on the triangle formed inside the unit circle.

The tangent of an angle (tan(θ°)) is the y-coordinate of point Q on the triangle which extends from the unit circle.

The trigonometric ratios are ratios between each pair of lengths in a right-angled triangle.

The opposite side of a right-angled triangle is the side which is opposite the marked angle.

The adjacent side of a right-angled triangle is the side which is next to both the right angle and the marked angle.

Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle containing the angle.

The tangent of an angle (tan(θ°)) is the y-coordinate of point Q of the triangle which extends from the unit circle.

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