CBSE

MATHEMATICS · Multi-part · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

Let f(x)=cos⁡xf(x)=\cos x. (i) Draw the graph of f(x)f(x) for the interval −2π≤x≤0-2\pi \le x \le 0, clearly indicating intercepts and extreme points. (ii) From the graph obtained, determine how many solutions the equation cos⁡x=−12\cos x = -\dfrac{1}{2} possesses in −2π≤x≤0-2\pi \le x \le 0, and list all such solutions. (iii) Using the periodic nature of the cosine function, write the general solution of cos⁡x=−12\cos x = -\dfrac{1}{2} for all real xx.

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