Mathematics: The terminal point of 0 is (3/2, 1/2). what is sin 0 ?

The terminal point of 0 is (3/2, 1/2). what is

Ответ:

saskiat1155

12.05.2021

$\frac{1}{ \sqrt{10} }$

Step-by-step explanation:

$\bigg( \frac{3}{2}, \: \: \frac{1}{2} \bigg) = (x, \: y) \\ \\ \implies \: x = \frac{3}{2} \: \: y = \frac{1}{2} \\ \\ r = \sqrt{ {x}^{2} + {y}^{2} } \\ = \sqrt{ { \bigg( \frac{3}{2} } \bigg)^{2} + { \bigg( \frac{1}{2} } \bigg)^{2}} \\ = \sqrt{ \frac{9}{4} + \frac{1}{4} } \\ = \sqrt{ \frac{10}{4} } \\ r = \frac{ \sqrt{10} }{2} \\ \\ \sin \theta = \frac{y}{r} \\ \\ \sin \theta = \frac{ \frac{1}{2} }{ \frac{ \sqrt{10} }{2} } \\ \\ \sin \theta = \frac{1}{ \sqrt{10} }$