The orientation angle ϕ \phi\,ϕ of a precision solar tracker satisfies the equation
5sin(ϕ−60∘)+12cos(ϕ−60∘)=0 5 \sin(\phi - 60^\circ) + 12 \cos(\phi - 60^\circ) = 0 5sin(ϕ−60∘)+12cos(ϕ−60∘)=0Determine all possible values of ϕ \phi\,ϕ in the range 0∘<ϕ<360∘0^\circ < \phi < 360^\circ0∘<ϕ<360∘, giving your answers to one decimal place.
Show that the equation
3sin3α=10sinα−7sinαcosα 3 \sin^3 \alpha = 10 \sin \alpha - 7 \sin \alpha \cos \alpha 3sin3α=10sinα−7sinαcosαcan be expressed in the form
sinα(kcos2α+mcosα+n)=0 \sin \alpha (k \cos^2 \alpha + m \cos \alpha + n) = 0 sinα(kcos2α+mcosα+n)=0where k,m k, m\,k,m and n n\,n are constants to be determined.
Hence find the exact solutions of the equation
3sin3α=10sinα−7sinαcosα 3 \sin^3 \alpha = 10 \sin \alpha - 7 \sin \alpha \cos \alpha 3sin3α=10sinα−7sinαcosαfor −π≤α≤π-\pi \le \alpha \le \pi−π≤α≤π.
