The graphs of and are commonly referred to as the sine curve and the cosine curve…
MATHEMATICS · Multi-part · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions
Problem
The graphs of y=sinθ and y=cosθ are commonly referred to as the sine curve and the cosine curve respectively.
(i) State the domain and the range of each curve when θ is measured in radians.
(ii) Explain with reasons whether each curve is an even function, an odd function, or neither. State the symmetry shown by the curve in each case.
(iii) Define the principal period of a trigonometric function. Hence write the period of sinθ and cosθ.
(iv) Describe how the graph of y=cosθ can be obtained by a horizontal translation of the graph of y=sinθ. State the magnitude and direction of the shift in terms of π.