whats the exact value of (cot240) (tan240)

Question

whats the exact value of (cot240) (tan240)

Answer 1

We need to find the smallest angle equivalent to 240 degrees that lies in the interval  0° ≤ θ ≤ 360°.  We do this by subtracting 240 from 360.

 

360 - 240 = 120

 

 

Now we subtract 120 from 180.

 

180 - 120 = 60

 

Our smallest angle is 60 degrees.

 

 

Remember that tanθ = sinθ / cosθ

 

 

(cot60)(tan60) =

 

(cos60 / sin60)*(sin60 / cos60) =

 

((1/2) / √(3)/2)*(√(3)/2 / (1/2))  =  1

 

Answer 2

cot(x) = 1/tan(x)

 

So:

 

cot(240)*tan(240) = tan(240)/tan(240) = 1