It is given that
f(x)=3cosx−4sinxf(x) = 3\cos x - 4\sin xf(x)=3cosx−4sinx
and that f(x)=Rcos(x+α)f(x) = R\cos(x + \alpha)f(x)=Rcos(x+α), where R>0 R > 0\,R>0 and 0°≤α≤90°0° \leq \alpha \leq 90°0°≤α≤90°.
Find the value of R R\,R and the value of α\alphaα, giving α \alpha\,α to one decimal place.
Hence solve, for 0°≤x≤360°0° \leq x \leq 360°0°≤x≤360°, the equation
3cosx−4sinx=13\cos x - 4\sin x = 13cosx−4sinx=1
Give your answers to one decimal place.
225 exam-style questions on WJEC A Level Maths 3.5 Trigonometry (A-level only), covering 3.5.1 Trigonometry (A-level only), 3.5.2 Trigonometry (A-level only), 3.5.3 Trigonometry (A-level only), 3.5.4 Trigonometry (A-level only), 3.5.5 Trigonometry (A-level only), 3.5.6 Trigonometry (A-level only), 3.5.7 Trigonometry (A-level only), and 3.5.8 Trigonometry (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.