1. Trig
Equations

2. 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 , °<𝑥≤360°
g x =−tan 𝑥+30 , −360°<𝑥≤0°
h x =−2sin 𝑥−90 , −180°<𝑥≤180°
Check using Desmos / geogebra

3. 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

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) = 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

5. Work out what value would make either bracket 0
WB31 solve Quadratic Equations given to you using Sin, Cos or Tan
Solve 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

6. 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

7. Work out what value would make 0
WB33 solve Quadratic Equations given to you using Sin, Cos or Tan
Solve 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 = gives
𝜃=19.5°, 160.5°,

8. 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 = 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= gives
x=60°, 300°

9. 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= , ≤𝜃≤180

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

11. END