​ What is the value of cos(−θ) ?

By the Pythagorean identity...

 

sin²(-θ) + cos²(-θ)   =   1

                                             Plug in  (-3/5)  for  sin(-θ)

(-3/5)² + cos²(-θ)   =   1

 

9/25   +  cos²(-θ)   =   1

                                             Subtract  9/25  from both sides of the equation.

cos²(-θ)   =   1  -  9/25

 

cos²(-θ)   =   16/25

                                             Take the  ±  square root of both sides.

cos(-θ)   =   ±√[ 16/25 ]

 

cos(-θ)   =   ± 4 / 5

 

Since  sin(-θ)  is negative,  -θ  must lie in Quadrant III or Quadrant IV.

Since  tan θ  is positive,  θ  must lie in Quadrant I or III, and so  -θ  must lie in Quadrant II or IV.

 

So  -θ  must lie in Quadrant IV, and  cos(-θ)  must be positive.

 

cos(-θ)   =   4 / 5