Find the tan θ when sin θ= -cos θ and θ is in quadrant iv

Step-by-step explanation:

sin θ= - cos θ

if :    cos θ  ≠  0  

you have :   tan θ = -1

 tan θ = - tan π/4

    tan θ = tan(- π/4 )

θ = - π/4 +kπ       k ∈ Z  

calculate: k   when θ is in quadrant IV :  3π /2 ≤ θ ≤2π

3π /2 ≤  - π/4 +kπ ≤2π

add π/4:         3π /2 + π/4 ≤  - π/4 +kπ+π/4  ≤2π +π/4

                     7π/4 ≤ kπ  ≤9π/4

                   7/4 ≤ k ≤9/4

                  1.75 ≤ k ≤ 2.25

 k ∈ Z  : k =2

so :  θ = - π/4 +2π

     θ = 7π/4

θ = 7(180°)/4 = 315°