square square Calculate the value of cosalpha if sinalpha =-0,8 and 270^circ lt alpha lt 360^circ

To find the value of $\cos\alpha$ given that $\sin\alpha = -0.8$ and $270^\circ < \alpha < 360^\circ$, we can use the Pythagorean identity for trigonometric functions.<br /><br />The Pythagorean identity states that for any angle $\alpha$, the following equation holds:<br /><br />$\sin^2\alpha + \cos^2\alpha = 1$<br /><br />Given that $\sin\alpha = -0.8$, we can substitute this value into the equation:<br /><br />$(-0.8)^2 + \cos^2\alpha = 1$<br /><br />Simplifying the equation, we get:<br /><br />$0.64 + \cos^2\alpha = 1$<br /><br />Subtracting 0.64 from both sides, we have:<br /><br />$\cos^2\alpha = 0.36$<br /><br />Taking the square root of both sides, we get:<br /><br />$\cos\alpha = \pm 0.6$<br /><br />Since the angle $\alpha$ is in the fourth quadrant ($270^\circ < \alpha < 360^\circ$), the cosine function is positive in this quadrant. Therefore, the value of $\cos\alpha$ is:<br /><br />$\cos\alpha = 0.6$<br /><br />So, the value of $\cos\alpha$ is 0.6.