AC9M9SP01 Year 9 Mathematics

This Content Descriptor from Year 9 Mathematics provides the specific knowledge and skills students should learn. Use it to plan lessons, create learning sequences, and design assessments that align with the Australian Curriculum v9.

recognise the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles using properties of similarity

Elaborations

• 1 understanding the terms “base”, “altitude”, “hypotenuse”, and “adjacent” and “opposite” sides to an angle, in a right-angled triangle, and identifying these for a given right-angled triangle
• 2 investigating patterns to reason about nested similar triangles that are aligned on a coordinate plane, connecting ideas of parallel sides and identifying the constancy of ratios of corresponding sides for a given angle
• 3 establishing an understanding that the sine of an angle can be considered as the length of the altitude of a right-angled triangle with a hypotenuse of length one unit and similarly the cosine as the length of the base of the same triangle, and relating this to enlargement and similar triangles
• 4 relating the tangent of an angle to the altitude and base of nested similar right-angled triangles, and connecting the tangent of the angle at which the graph of a straight line meets the positive direction of the horizontal coordinate axis to the gradient of the straight line

Related Achievement Standards