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°