Question

When a angle is in third quadrant tanteta=3 then sinteta=

Answer 1

tan Ф = 3       sin Ф/ cos Ф = 3
sin Ф = 3 cos Ф           sin² Ф = 9 cos² Ф         
sin ² Ф  = 9 - 9 sin² Ф  => sin² Ф = 0.9  =>  sin Ф = - √0.9
- ve because sin is -ve in  3rd quadrant  180 < Ф <= 270 degrees

Answer 2

Let the angle be 'α'
tanα = 3 
w.k.t.
tanα = opp side / adj side
       = 3/1
If we consider a right angled triangle having sides 3 n 1 units, then we get √10 as hypotenuse.
therefore, sinα = opp side / hypotenuse
                      = 3/√10
But α is in third quadrant.
therefore, sinα = -3/√10