Consider the three fundamental trigonometric functions y=sinx, y=cosx and y=tanx. Answer the following questions related to their graphical properties:
(i) State the domain and range of each of the three functions.
(ii) Write the principal period of each function.
(iii) Explain, with reference to the unit circle, why the period of tanx is π and not 2π like sinx and cosx.
(iv) Describe how the graph of y=cosx can be obtained from the graph of y=sinx without changing its shape.