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By factorising, or otherwise, solve the following equations for 0≤θ≤360:

  1. tan2⁡(θ)+3tan⁡(θ)−10=0
  2. 9cos2⁡(θ)−6cos⁡(θ)+1=0
  3. 4sin2⁡(θ)−9sin⁡(θ)+2=0

For (a), let t=tan⁡(θ). Can you solve

t2+3t−10=0

?


For (b), let c=cos⁡(θ) and consider

9c2−6c+1=0
4s2−9s+2=(s−2)(4s−1)

Note that −1≤sin⁡(θ)≤1 so sin⁡(θ)=2 does not lead to any solutions.