solve the equation on the interval 0≤θ<2π

Question

cos(θ/3−π/4)=1/2

Answer 1

solve the equation on the interval 0≤θ≤2π. cos(θ/3 - π/4) = 1/2

to isolate θ, take the inverse cosine of both sides:

1. (θ/3 - π/4) = cos^-1(1/2) Then add π/4 to both sides, and multiply both sides by 3
2. θ/3 = cos^-1(1/2) + π/4
3. θ = 3(cos^-1(1/2)) + π/4
4. θ = 3(60 + 45)
5. θ =315°