Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
A string is wound around a circle and then unwound while being held taut. The curve traced by the point P at the end of the siring is called the involute of the circle. If the circle has radius r and center O and the initial position of P is (r, 0), and if the parameter θ is chosen as in the figure, show that parametric equations of the involute are
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