How to evaluate value of sin (300)+tan(210)?

Question

How to evaluate value of $sin (300^circ)+tan(210^circ)$ ?

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Answer 1 · 2018-05-11T17:11:04

$sin300^circ+tan210^circ=-1/(2sqrt3)~~-0.2887$

Here,

$sin300^circ=sin(360^circ-60^circ)...toIV^(th)Quadrant$

$color(white)(sin300^circ)=-sin60^circ...tosin < 0$

$color(white)(sin300^circ)=-sqrt3/2$

We have,

$tan210^circ=tan(180^circ+30^circ)...toIII^(rd)Quadrant$

$color(white)(tan210^circ)=tan30^circ...totan > 0$

$color(white)(tan210^circ)=1/sqrt3$

So,

$sin300^circ+tan210^circ=-sqrt3/2+1/sqrt3=-(sqrt3/2-1/sqrt3)$

$sin300^circ+tan210^circ=-(3- 2)/(2sqrt3)=-1/(2sqrt3)~~-0.2887$