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Question:- Prove that, θ (theta) is a constant angle.​

Answer 1

Answer:

Here we will discuss about radian is a constant angle. Let O be the centre of a circle and radius OR = r. If we take an arc AB = OA = r, then by definition, ∠AOB =1 radian.

Let AO be produced to meet the circle at the point C. Then the length of the arc ABC half the circumference and ∠AOC, the angle at the centre subtended by this arc = a straight angle = two right angles.

Now if we take the ratio of the two arcs and that of the two angles, we have

arc AB/arc ABC = r/(1/2 × 2∙π∙r) = 1/ π

∠AOB/∠AOC = 1 radian/2 right angles



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But in geometry, we can show that an arc of a circle is proportional to the angle it subtends at the centre of the circle.

Step-by-step explanation:

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