Question

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

Answer 1

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°