Question

Which angle has a sine of -1/2 and a cosine of -√3/2

Answer 1

`\sin x=-(1)/(2) < 0\\\\\cos x=-(\sqrt3)/(2) < 0\\\\therefore\ x\in(180^o;\ 270^o)`


`\text{We know:}\ \tan x=(\sin x)/(\cos x)\\\\\text{therefore:}\ \tan x=(-(1)/(2))/(-(\sqrt3)/(2))=(1)/(2)\cdot(2)/(\sqrt3)=(1)/(\sqrt3)\cdot(\sqrt3)/(\sqrt3)=(\sqrt3)/(3)`


`\tan x=(\sqrt3)/(3)\Rightarrow x=30^o+180^o\cdot k;\ k\in\mathbb{Z}`


`x\in(180^o;\ 270^o)\ therefore\ \boxed{x=30^o+180^o=210^o}`