use the given conditions to find the exact value of the expression: sin(a)=(-5/13), tan(a)> 0, sin[a-(2pi/3)

Question

use the given conditions to find the exact value of the expression: sin(a)=(-5/13), tan(a)> 0, sin[a-(2pi/3)

Answer 1

As per given conditions angle a is in third quadrant

sin[a-(2pi/3)]=

sin(a)cos(2pi/3)-cos(a)sin(2pi/3)

 

Substituting values

 

(-5/13)(-1/2)-(-12/13)(sqrt(3)/2)

 

(5/26)+12 sqrt(3)/26

 

[5+12sqrt(3)]/26