Cos =0,8 3π/2

Given that \(\cos a = 0.8\) and the angle \(a\) is in the interval \(\frac{3\pi}{2} < a < 2\pi\), we can find the sine and cotangent values. 1. **Identify the quadrant**: - The interval \(\frac{3\pi}{2} < a < 2\pi\) indicates that angle \(a\) is in the fourth quadrant, where sine is negative and cosine is positive. 2. **Use the Pythagorean identity**: \[ \sin^2 a + \cos^2 a = 1 \] Substituting the known value of \(\cos a\): \[ \sin^2 a + (0.8)^2 = 1 \\ \sin^2 a + 0.64 = 1 \\ \sin^2 a = 1 - 0.64 \\ \sin^2 a = 0.36 \\ \sin a = -\sqrt{0.36} = -0.6 \] (We take the negative root since \(a\) is in the fourth quadrant!) 3. **Calculate cotangent**: \[ \cot a = \frac{\cos a}{\sin a} \] Substituting the values of \(\cos a\) and \(\sin a\): \[ \cot a = \frac{0.8}{-0.6} = -\frac{4}{3} \] To summarize: - \(\sin a = -0.6\) - \(\cot a = -\frac{4}{3}\) Thus, the values are: - \(\sin a = -0.6\) - \(a\) in radians can be calculated as \(a \approx 5.36\) (you can calculate the exact angle in radians using inverse cosine, but within the fourth quadrant and in the specified interval). - \(\cot a = -\frac{4}{3}\)