recognise the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles using properties of similarity
Elaborations
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
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
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
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
Code
VC2M9SP01
Curriculum resources and support
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