Using the identity sin26 sin^2Theta cos^2Theta = the value of cosTheta to the nearest hundredth , if sin26 sinTheta =-0.79 and pi lt Theta lt (3pi )/(2) Answer Attemptiout of 2

We are given that $\sin\Theta = -0.79$ and $\pi < \Theta < \frac{3\pi}{2}$. We are asked to find the value of $\cos\Theta$.<br /><br />We use the trigonometric identity $\sin^2\Theta + \cos^2\Theta = 1$.<br />Substituting the given value of $\sin\Theta$, we have:<br />$(-0.79)^2 + \cos^2\Theta = 1$<br />$0.6241 + \cos^2\Theta = 1$<br />$\cos^2\Theta = 1 - 0.6241$<br />$\cos^2\Theta = 0.3759$<br />$\cos\Theta = \pm\sqrt{0.3759}$<br />$\cos\Theta \approx \pm 0.6131$<br /><br />Since $\pi < \Theta < \frac{3\pi}{2}$, $\Theta$ is in the third quadrant. In the third quadrant, both sine and cosine are negative. Therefore, we take the negative value for $\cos\Theta$.<br /><br />$\cos\Theta \approx -0.6131$<br /><br />Rounding to the nearest hundredth, we get:<br />$\cos\Theta \approx -0.61$<br /><br />Final Answer: The final answer is $\boxed{-0.61}$<br />