Question

The point A(sinq, cosq) is 3 units away from the point B (2cos75⁰, 2sin75⁰). If 0⁰£q< 360⁰, then q is-

• A. 15⁰
• B. 165⁰
• C. 195⁰
• D. 255⁰

Answer 1

Answer: (C)

195⁰

Answer 2

Since, AB = 3

Ž $\sqrt{(2\cos 75º - \sin\theta)^{2} + (2\sin 75º - \cos\theta)^{2}}$ = 3

Ž $\sqrt{4 + 1 - 4\sin(\theta + 75º)}$ = 3

Ž 5 – 4sin(q + 75⁰) = 9 Ž sin(q + 75⁰) = –1

Ž q + 75⁰ = 270⁰ Ž q = 195⁰