## Core concept 3.2: Trigonometry

### Similar triangles using ratio tables

3.2.1.1* Understand that the trigonometric functions are derived from measurements within a unit circle

3.2.1.2 Recognise the right-angled triangle within a unit circle and use proportion to scale to similar triangles

3.2.1.3* Know how the sine, cosine and tangent ratios are derived from the sides of a right-angled triangle

secmm-cc-theme-3-key-idea-28.pptx

### 3.2.1.1 Understand that the trigonometric functions are derived from measurements within a unit circle

Identify a triangle within the unit circle and understand that the hypotenuse is the only side with a constant length.

Understand that the height and length of the base of the triangle do not change in a linear way as the point moves around the circle’s edge.

3.2.2.1 Choose appropriate trigonometric relationships to use to solve problems in right-angled triangles

3.2.2.2 Use trigonometric ratios to find a missing side in a right-angled triangle

3.2.2.3 Use trigonometric ratios to find a missing angle in a right-angled triangle

secmm-cc-theme-3-key-idea-29.pptx

Tangent:   tanθ is the height of the opposite side that is the tangent to the unit circle at the point x=1.

Use similar triangles from the unit circle to define tanθ.