2 (a) When \( \sin x^{\circ}=0.36 \), find the acute angle \( x^{\circ} \). \[ \frac{\sin x}{0}=\frac{0.36}{0.36} \] (b) When \( \sin x^{\circ}=0.36 \), find the obtuse angle \( x^{\circ} \).

To solve the problem where \( \sin x^{\circ} = 0.36 \), we'll find both the acute and obtuse angles \( x^{\circ} \). ### Part (a): Finding the Acute Angle The **acute angle** is the angle between \( 0^\circ \) and \( 90^\circ \) whose sine is 0.36. To find this angle, we use the inverse sine function: \[ x = \sin^{-1}(0.36) \] Using a calculator: \[ x \approx 21.1^\circ \] ### Part (b): Finding the Obtuse Angle The **obtuse angle** is the angle between \( 90^\circ \) and \( 180^\circ \) that also has a sine of 0.36. Since the sine function is positive in both the first and second quadrants, the obtuse angle can be found by: \[ x = 180^\circ - \sin^{-1}(0.36) \] Using the acute angle found in part (a): \[ x = 180^\circ - 21.1^\circ = 158.9^\circ \] ### Summary of Results - **Acute angle:** \( x \approx 21.1^\circ \) - **Obtuse angle:** \( x \approx 158.9^\circ \)