6. If \( \sin A=3 / 5 \) then find the value \( \cot A \). 7. What do we call the opposite side of

To find \( \cot A \) when \( \sin A = \frac{3}{5} \), we can use the Pythagorean identity. Since \( \sin^2 A + \cos^2 A = 1 \), we can first find \( \cos A \). For \( \sin A = \frac{3}{5} \), we have \( \cos A = \sqrt{1 - \left(\frac{3}{5}\right)^2} = \sqrt{1 - \frac{9}{25}} = \sqrt{\frac{16}{25}} = \frac{4}{5} \). Now, \( \cot A = \frac{\cos A}{\sin A} = \frac{\frac{4}{5}}{\frac{3}{5}} = \frac{4}{3} \). The side opposite to angle \( A \) in a right triangle is an important concept in trigonometry! This side is the one directly across from angle \( A \), and it plays a pivotal role in defining the sine function, as \( \sin A \) is the ratio of the length of the opposite side to the hypotenuse. So, if you visualize a right triangle, the opposite side is your go-to for finding sine values!