Question

If 5x + 12y + 13 = 0 is transformed into xcosα + ysinα = p, then α = ? α ∊ [– π, π]

(a) cos^–1[– (5/13)]

(b) sin^–1[– (12/13)]

(c) tan^–1 (12/5) – π

(d) tan^–1(12/5)

Answer 1

The correct option (c) tan^–1 (12/5) – π

Explanation:

line: 5x + 12y + 13 = 0

∴ – (5/13)x – (12/13)y = 1

comparing with xcosα + ysinα = p,

we get cosα = – (5/13), sinα = – (12/13)

∴ tanα = (12/5)

as α ∈ [– π, π] i.e. in 3rd quadrant 

∴ α = tan^–1(12/5) – π