Question

what is the value of tan 480 degrees .explain with procedure please

Answer 1

tan 480 = tan (360+120) = tan 120. here as the tan will fall in 2nd quadrant it will be negative. therefore tan120 = tan(180-60) = -tan 60 -√3.

Answer 2

Answer:

$\text{The value of }\tan 480^{\circ} \text{ is }-\sqrt3$  

Step-by-step explanation:

Given the angle 480°

we have to find the value of tan 480°

As in first quadrant all the trigonometric ratios are positive i.e

$\tan(360+\theta)=\tan \theta$

Therefore, we can write

$\tan 480^{\circ}=\tan(360^{\circ}+120^{\circ}=\tan 120^{\circ}$

$As, \tan(90^{\circ}+\theta)=-\cot \theta$    

( ∵ tangent is negative in second quadrant)

$\tan 480^{\circ}=\tan120^{\circ}=\tan(90^{\circ}+30^{\circ})=-\cot 30^{\circ}$

$=-\frac{1}{\tan 30^{\circ}}=-\frac{1}{\frac{1}{\sqrt3}}=-\sqrt 3=-1.732$

$\text{The value of }\tan 480^{\circ} \text{ is }-\sqrt3$