The graphs of the sine and cosine functions exhibit special kinds of symmetry often…

MATHEMATICS · Multi-part · ISC · Mathematics · Sets and Functions · Sets and Functions

Problem

The graphs of the sine and cosine functions exhibit special kinds of symmetry often described as “odd” and “even”. (i) Define an odd function and an even function, giving one standard algebraic example of each. (ii) Sketch the graphs of y=sin⁡xy=\sin x and y=cos⁡xy=\cos x for x∈[−2π,2π]x\in[-2\pi,2\pi]. Explain, by referring to corresponding points on the graphs, why sin⁡x\sin x is odd while cos⁡x\cos x is even. (iii) From the definition of odd and even functions, state the precise relationship between sin⁡x\sin x and sin⁡(−x)\sin(-x), and between cos⁡x\cos x and cos⁡(−x)\cos(-x). Briefly describe how this symmetry helps when evaluating trigonometric functions at negative angles.

Related theory

Browse the problem library