1 Press Ctrl-A ©G Dear 2010 – Not to be sold/Free to use Angles between two lines. Stage 6 - Year 11 Mathematic Extension 1 (Preliminary)

2 m1m1 m2m2 End of Slide Finding the angle, θ. Between two lines. θ f(x) x tan θ = m 1 – m 2 1 – m 1 m 2 α β

3 End of Slide Proof: tan θ = m 1 – m 2 1 – m 1 m 2 β θ f(x) x α m 1 = tan β, m 2 = tan α, β = α + θ [ External Angle ]  θ = β - α tan θ = tan ( β – α) tan β – tan α 1 – tan α tan β = m 1 – m 2 1 – m 1 m 2 = tan θ >0 θ acute tan θ <0 θ obtuse m 1 – m 2 1 – m 1 m 2 = For the acute angle …

4 tan -1 ( ) End of Slide tan θ = m 1 – m 2 1 – m 1 m 2 θ f(x) x Find the angle between the lines 2x – y + 1 = 0 and 2x + y - 3 = 0 y = 2x + 1 x–y+1=0 2x+y-3=0 m1 = 2m1 = 2 and y = -2x + 3 m 2 = -2 tan θ = 2 – (-2) 1 – 2(-2) tan θ = 0.8 tan -1 (0.8) tan θ = m 1 – m 2 1 – m 1 m 2 θ = 38 o 40’