2. if \\( \\sin \\theta = \\frac { 3 } { 7 } \\), find the value of \\( \\theta \\)

Explanation:

Step1: Use inverse sine function

Given (\sin\theta=\frac{3}{7}), we use the inverse - sine function (\theta = \sin^{-1}(x)). Here (x = \frac{3}{7}). So (\theta=\sin^{-1}(\frac{3}{7}))

Step2: Calculate the value

Using a calculator, (\sin^{-1}(\frac{3}{7})\approx25.37^{\circ}) (in degree mode) or (\sin^{-1}(\frac{3}{7})\approx0.443) radians (in radian mode)

Answer:

If we consider the value in degrees, (\theta\approx25.37^{\circ}); if in radians, (\theta\approx0.443)