Trig Equations

f(x)= cos 𝑥 2 , 0°<𝑥≤360° g x =−tan 𝑥+30 , −360°<𝑥≤0° Trigonometry KUS objectives BAT rearrange and solve trig equations BAT Starter: sketch these graphs f(x)= cos 𝑥 2 , 0°<𝑥≤360° g x =−tan 𝑥+30 , −360°<𝑥≤0° h x =−2sin 𝑥−90 , −180°<𝑥≤180° Check using Desmos / geogebra

Solve sin 𝜃 =2 cos 𝜃 in the interval 0≤ 𝜃 ≤360° WB29 Solve sin 𝜃 =2 cos 𝜃 in the interval 0≤ 𝜃 ≤360° Divide by Cosθ Use Trig Identities Use Tan-1 2 y = Tanθ 90 180 270 360 63.4 243.4

Solve 𝑠𝑖𝑛 2 (𝜃−30) = 1 2 in the interval 0≤ 𝜃 ≤360° WB30 solve Quadratic Equations given to you using Sin, Cos or Tan Solve 𝑠𝑖𝑛 2 (𝜃−30) = 1 2 in the interval 0≤ 𝜃 ≤360° Work out the acceptable range. Subtract 30 Square root both sides. On fractions root top and bottom separately. Can be positive or negative. 45 135 1/√2 y = Sinθ -1/√2 90 180 270 360 225 315 360 added to get a value in the range

Work out what value would make either bracket 0 WB31 solve Quadratic Equations given to you using Sin, Cos or Tan Solve 2 𝑐𝑜𝑠 2 𝜃 − cos 𝜃 −1 =0 in the interval 0≤ 𝜃 ≤360° Factorise Work out what value would make either bracket 0 360 1 Cosθ = 1 has 2 solutions y = Cosθ -0.5 Cosθ = -0.5 has 2 solutions 90 180 270 360 120 240

Work out what value would make either bracket 0 WB32 solve Quadratic Equations given to you using Sin, Cos or Tan Solve 𝑠𝑖𝑛 2 𝜃 −3 sin 𝜃 +2=0 in the interval 0≤ 𝜃 ≤360° Factorise Work out what value would make either bracket 0 2 Sinθ = 2 has no solutions 90 1 Sinθ = 1 has 1 solution y = Sinθ 90 180 270 360

Work out what value would make 0 WB33 solve Quadratic Equations given to you using Sin, Cos or Tan Solve 3 𝑠𝑖𝑛 2 𝜃 + sin 𝜃 =0 in the interval 0≤ 𝜃 ≤360° 3 𝑠𝑖𝑛 2 𝜃 + sin 𝜃 =0 Factorise sin 𝜃 3 sin 𝜃 +1 =0 Work out what value would make 0 sin 𝜃 =0 or sin 𝜃 = 1 3 sin 𝜃 =0 gives 𝜃=90° sin 𝜃 = 1 3 gives 𝜃=19.5°, 160.5°,

4 𝑠𝑖𝑛 2 𝑥 +2=10 cos 𝑥 cos 𝑥 = 1 2 or cos 𝑥 =−3 WB34 exam Q Solve for 0≤ θ ≤360°   all the solutions of 4 sin 2 x +2=10 cos x You must show clearly how you obtained your answers   4 𝑠𝑖𝑛 2 𝑥 +2=10 cos 𝑥 cos 𝑥 = 1 2 or cos 𝑥 =−3 4 −4 𝑐𝑜𝑠 2 𝑥 +2=10 cos 𝑥 4 𝑐𝑜𝑠 2 𝑥 +10 cos 𝑥 −6=0 cos 𝑥 =−3 gives 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠 2 𝑐𝑜𝑠 2 𝑥 +5 cos 𝑥 −3=0 2 cos 𝑥 −1 cos 𝑥 +3 =0 cos 𝑥= 1 2 gives x=60°, 300°

𝑡𝑎𝑛 2 𝜃−𝑡𝑎𝑛𝜃=0, 0≤𝜃≤360 2sin 𝜃−𝑐𝑜𝑠𝜃=0, 0≤𝜃≤180 Practice 3 Solve these equations 2sin 𝜃−𝑐𝑜𝑠𝜃=0, 0≤𝜃≤180 𝑡𝑎𝑛 2 𝜃−𝑡𝑎𝑛𝜃=0, 0≤𝜃≤360 4 𝑐𝑜𝑠 2 𝜃+3 sin 𝜃 =4, 0≤𝜃≤360 𝑠𝑖𝑛 2 𝜃= 1 4 , 0≤𝜃≤180

One thing to improve is – KUS objectives BAT rearrange and solve trig equations self-assess One thing learned is – One thing to improve is –

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