For the three standard trigonometric functions

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

For the three standard trigonometric functions y=sin⁡xy=\sin x, y=cos⁡xy=\cos x and y=tan⁡xy=\tan x, respond to the following items. (i) Define the period of a real-valued function. Hence state the fundamental period of each of the three functions mentioned above. (ii) Explain, with reason, why the ranges of sin⁡x\sin x and cos⁡x\cos x are identical while the range of tan⁡x\tan x is different. (iii) Describe the complete domain of tan⁡x\tan x, making clear reference to the points where the function is not defined.

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