How do you evaluate $tan 300$ $tan300$ ?

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Answer 1 · 2016-06-18T04:17:29

${tan 300}^{o} = - \sqrt{3}$ $tan300^o=-sqrt3$

It is presumed that by $tan 300$ $tan300$ it is meant to be ${tan 300}^{o}$ $tan300^o$ .

As adding or subtracting multiples of $2 π$ $2pi$ radians or $360^{o}$ $360^o$ does not change the trigonometric ratio

${tan 300}^{o} = tan (360^{o} - 60^{o}) = tan (- 60^{o})$ $tan300^o=tan(360^o-60^o)=tan(-60^o)$

Further as $tan (- θ) = - tan θ$ $tan(-theta)=-tantheta$

${tan 300}^{o} = tan (- 60^{o}) = - {tan 60}^{o} = - \sqrt{3}$ $tan300^o=tan(-60^o)=-tan60^o=-sqrt3$

How do you evaluate tan300tan300?