41 a C1 2 C1 for communicating effectively how the sine and cos M tan = sin ÷ cos x x x can be used to find tan (This could be tan = ) ÷ x = = M1 for correct use of tan M1 = = 1 A1 for correct combination of surds A1 tan–1 1 = 45° b Alternatively, use theorem to Pythagoras’ work out the length of the third side, e.g. (side)2 = 16 8 = 8 A1 for tan = 1 x – A1 side = tan = 1 x tan = = 1 x tan-1 1 = 45° M1 for use of inverse tan or recognising an isosceles triangle M1 A1 for 45° A1 45° 6 42 Using theorem, M1 2 M1 for correct Pythagoras statement M Pythagoras’ the hypotenuse = = = 4 A1 A1 for 4 Then sin = x B1 B1 for correct sin x and cos = x Hence (sin + (cos = x)2 x)2 B1 B1 for correct cos x + = = 1 C1 C1 for correct explanation 5
41 a b tan x = sin x ÷ cos x ÷ = = = = 1 tan–1 1 = 45° Alternatively, use Pythagoras’ theorem to work out the length of the third side, e.g. (side)2 = 16 – 8 = 8 side = tan x = = 1 tan-1 1 = 45° tan x = 1 45° C1 M1 A1 A1 M1 A1 2 C1 for communicating effectively how the sine and cos can be used to find tan (This could be tan x = ) M1 for correct use of tan A1 for correct combination of surds A1 for tan x = 1 M1 for use of inverse tan or recognising an isosceles triangle A1 for 45° M 6 42 Using Pythagoras’ theorem, the hypotenuse = = = 4 Then sin x = and cos x = Hence (sin x)2 + (cos x)2 = + = = 1 M1 A1 B1 B1 C1 2 M1 for correct Pythagoras statement A1 for 4 B1 for correct sin x B1 for correct cos x C1 for correct explanation M 5
Higher_Skills_Geometry_MarkScheme_Edexcel.docx