The graph of y=sinxy=\sin xy=sinx is translated π6\displaystyle \frac{\pi}{6}6π in the positive x x\,x direction, stretched by scale factor 4 in the y y\,y direction and translated 5 in the positive y y\,y direction. Determine the equation of the resulting graph in the form y=asinx+bcosx+cy=a\sin x+b\cos x+cy=asinx+bcosx+c.
The minimum value of 123sinx−2cosx+5\displaystyle \frac{1}{2\sqrt3\sin x-2\cos x+5}23sinx−2cosx+51 is 19\displaystyle \frac1991. Calculate the maximum value of 23sinx−2cosx+52\sqrt3\sin x-2\cos x+523sinx−2cosx+5.
348 exam-style questions on Edexcel A Level Maths Trigonometry and Modelling, covering 7.1 Addition Formulae, 7.2 Double Angle Formulae, 7.3 Solving Trigonometric Equations, 7.4 Simplifying a cos x +- b sin x, 7.5 Proving Trigonometric Identities, and 7.6 Modelling with Trigonometric Functions. Each one has a worked solution and a mark scheme showing where the marks go.