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

Answer:Step-by-step explanation:sin θ= - cos θif :    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 ≤2π3π /2 ≤  - π/4 +kπ ≤2πadd 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 =2so :  θ = - π/4 +2π      θ = 7π/4 θ = 7(180°)/4 = 315°