PainterGuy
- 938
- 72
- Homework Statement
- How do I solve cos(a+θ)=0?
- Relevant Equations
- Please check the posting.
Hi,
I was trying to solve y=cos(α+θ) where α is a constant and θ has range [0,2π).
If α=3 is assumed, the solution is as shown below and it makes sense
\theta_{1}=\frac{3}{2}(\pi-2)
\theta_{2}=\frac{1}{2}(5 \pi-6)
But if I don't use any specific value for α, the solution doesn't make sense to me.
\pi n-\frac{5 \pi}{2} \leq \alpha \leq \pi n-\frac{\pi}{2} and \theta=\pi\left(n-\frac{1}{2}\right)-\alpha and n \in \mathbb{Z}
Source: https://www.wolframalpha.com/input/?i=solve+cos(α+θ)=0+for+θ+from+0+to+2pi
Somewhere I found the solution to be as shown below but don't understand why \cos ^{-1} y is used, and please note that α is not given any specific value:
\theta_{1}=\left(\cos ^{-1} \mathrm{y}\right)-\alpha
\theta_{2}=2 \pi-\left(\cos ^{-1} \mathrm{y}\right)-\alpha
Could you please help me? It's not homework but I still thought I better post it here nonetheless.
I was trying to solve y=cos(α+θ) where α is a constant and θ has range [0,2π).
If α=3 is assumed, the solution is as shown below and it makes sense
\theta_{1}=\frac{3}{2}(\pi-2)
\theta_{2}=\frac{1}{2}(5 \pi-6)
But if I don't use any specific value for α, the solution doesn't make sense to me.
\pi n-\frac{5 \pi}{2} \leq \alpha \leq \pi n-\frac{\pi}{2} and \theta=\pi\left(n-\frac{1}{2}\right)-\alpha and n \in \mathbb{Z}
Source: https://www.wolframalpha.com/input/?i=solve+cos(α+θ)=0+for+θ+from+0+to+2pi
Somewhere I found the solution to be as shown below but don't understand why \cos ^{-1} y is used, and please note that α is not given any specific value:
\theta_{1}=\left(\cos ^{-1} \mathrm{y}\right)-\alpha
\theta_{2}=2 \pi-\left(\cos ^{-1} \mathrm{y}\right)-\alpha
Could you please help me? It's not homework but I still thought I better post it here nonetheless.
Last edited: