3. Find the size of the angle \( \theta \) where \( \theta \) is acute. \( \begin{array}{ll}\text { a. } \sin \theta=0.529 & \text { c. } \tan \theta=1.8 \\ \text { b. } \cos \theta=0.493 & \text { d. } \cos \theta=0.5\end{array} \)

To find the size of the angle \( \theta \) where \( \theta \) is acute, we can use the inverse trigonometric functions. Given: a. \( \sin \theta = 0.529 \) b. \( \cos \theta = 0.493 \) c. \( \tan \theta = 1.8 \) d. \( \cos \theta = 0.5 \) We can use the inverse sine, inverse cosine, and inverse tangent functions to find the angle \( \theta \) in each case. Let's calculate the angle \( \theta \) for each given trigonometric function: Calculate the value by following steps: - step0: Calculate: \(\arcsin\left(0.529\right)\) Calculate or simplify the expression \( \arcsin(0.493) \). Calculate the value by following steps: - step0: Calculate: \(\arcsin\left(0.493\right)\) Calculate or simplify the expression \( \arctan(1.8) \). Calculate the value by following steps: - step0: Calculate: \(\arctan\left(1.8\right)\) Calculate or simplify the expression \( \arccos(0.5) \). Calculate the value by following steps: - step0: Calculate: \(\arccos\left(0.5\right)\) - step1: Calculate the trigonometric value: \(\frac{\pi }{3}\) The size of the angle \( \theta \) where \( \theta \) is acute for each given trigonometric function is as follows: a. \( \theta \approx 0.557422 \) radians b. \( \theta \approx 0.515535 \) radians c. \( \theta \approx 1.063698 \) radians d. \( \theta \approx 1.047198 \) radians Therefore, the size of the angle \( \theta \) where \( \theta \) is acute for each given trigonometric function is approximately the values calculated above.