Question Using the identity sin^2Theta +cos^2Theta =1 find the value of cosTheta to the nearest hundredth , if sinTheta =0.54 and 0lt Theta lt (pi )/(2) 0.08

We are given that $\sin\Theta = 0.54$ and $0 < \Theta < \frac{\pi}{2}$. We are asked to find the value of $\cos\Theta$ using the identity $\sin^2\Theta + \cos^2\Theta = 1$.<br /><br />Since $\sin\Theta = 0.54$, we have<br />$$ \sin^2\Theta = (0.54)^2 = 0.2916 $$<br />Substituting this into the identity, we get<br />$$ 0.2916 + \cos^2\Theta = 1 $$<br />$$ \cos^2\Theta = 1 - 0.2916 $$<br />$$ \cos^2\Theta = 0.7084 $$<br />Since $0 < \Theta < \frac{\pi}{2}$, $\Theta$ is in the first quadrant, where cosine is positive. Therefore, we take the positive square root:<br />$$ \cos\Theta = \sqrt{0.7084} $$<br />$$ \cos\Theta \approx 0.84 $$<br />Rounding to the nearest hundredth, we get $\cos\Theta \approx 0.84$.<br /><br />Final Answer: The final answer is $\boxed{0.84}$<br />