If and for real numbers and

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

If sin⁡θ=sin⁡ϕ\sin\theta = \sin\phi and cos⁡θ=cos⁡ϕ\cos\theta = \cos\phi for real numbers θ\theta and ϕ\phi, which one of the following relations must hold between θ\theta and ϕ\phi? (a) θ=nπ+ϕ,  n∈Z\theta = n\pi + \phi,\; n\in\mathbb Z (b) θ=−ϕ+2nπ,  n∈Z\theta = -\phi + 2n\pi,\; n\in\mathbb Z (c) θ=2nπ+ϕ,  n∈Z\theta = 2n\pi + \phi,\; n\in\mathbb Z (d) θ=(2n+1)π−ϕ,  n∈Z\theta = (2n+1)\pi - \phi,\; n\in\mathbb Z

Related theory

Browse the problem library