trighardquestions

today we are looking at hard questions in trig 4 spec

ex 4c §

show that $\cos 70+\sin 40=\cos 10$ no formula for it :( do we give up?

no

Never back down never WHAT!!!!!!

rearrange: $\cos 70-\cos 10=-\sin 40$ dont assume its true to begin with heres how to write it: consider $\cos 70-\cos 10$ $=-2\sin \frac{70+10}{2}\sin \frac{70-10}{2}$ $=-2\sin 40\sin 30$ $=-\sin 40$

12b §

solve $\sin 5\theta -\sin 3\theta +\sin \theta =0$ for $0\le \theta \le x$ $2\cos \left(\frac{5\theta +3\theta }{2}\right)\sin \left(\frac{5\theta -3\theta }{2}\right)$ $2\cos 4\theta \sin \theta +\sin \theta =0$ $\sin \theta (2\cos 4\theta +1)=0$ $\sin \theta =0\text{ or }2\cos 4\theta +1=0$ $\theta =0\text{ or }\pi \text{ and }\cos 4\pi =-\frac{1}{2}$ $4\theta =\frac{2\pi }{3},\frac{4\pi }{3},\frac{8\pi }{3},\frac{10\pi }{3}$ $\theta =\frac{\pi }{6},\frac{\pi }{3},\frac{2\pi }{3},\frac{5\pi }{6}$