Trignometry

Quote:

Originally Posted by lemontea

2) a,b (0,2pi)and sin (a)=sqrt(3)/2, cos(b)=-sqrt(3)/2, tan(a+b)=-1/sqrt(3), then give the exact value of a and b in terms of pi

a: ____pi b:_____pi

There are two angles such that $\sin(a)=\frac{\sqrt{3}}{2} \\\ a=\frac{\pi}{3}\mbox{ or }\frac{2\pi}{3}$

Also with cosine $\cos(b)=-\frac{3}{2} \\\ b=\frac{5\pi}{6} \mbox{ or } \frac{7\pi}{6}$

and $\tan(a+b)=-\frac{1}{\sqrt{3}} \\\ a+b=\frac{5\pi}{6} \mbox{ or } \frac{11\pi}{6}$

So for this to be true $a=\frac{2\pi}{3} \\\ b=\frac{7\pi}{6} \\\ a+b=\frac{11\pi}{6}$

Hint: for the first one $\sin^2\left( \sin^{-1}\left( \frac{4}{x}\right)\right)= \left[\sin\left(\sin^{-1}\left( \frac{4}{x}\right)\right)\right]^2$