Consider an arbitrary angle measured from the initial side.

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

Problem

Consider an arbitrary angle θ\theta measured from the initial side. (i) State how many degrees and how many radians correspond to one complete revolution. (ii) Describe, in words, a systematic procedure to write θ\theta in the form k×k \times (one complete revolution) + α+\, \alpha, where kk is an integer and 0≤α<360∘0 \leq \alpha < 360^{\circ}. (iii) For θ=−765∘\theta = -765^{\circ}, apply the procedure from part (ii) to determine the value of kk and the magnitude (in degrees) of α\alpha. Also specify whether the terminal side of α\alpha is reached by a clockwise or counter-clockwise rotation from the initial side.

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