Please explain the root cause to me ---**Question 1** It is given that $\sin \theta = \frac{1}{2}$. Molly says $\theta = 30$ radians. Do you agree with her? Explain your answer. Answer: I do not agree with her. $\theta = \sin^{-1}(0.5)$ is equal to 0.52359 radians. round 0.524 to 3 s.f. radians. 0.524 radians. \[2\]

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Let's examine this problem step by step. We're given that sine theta equals one half, and Molly claims that theta equals 30 radians. To understand if this is correct, we need to first recognize that 30 degrees does give us sine equals one half on the unit circle. The root cause of Molly's error is confusing degrees with radians. While 30 degrees does satisfy sine theta equals one half, we must convert to radians. Since 180 degrees equals pi radians, 30 degrees equals pi over 6 radians, which is approximately 0.524 radians, not 30 radians. Let's see what 30 radians actually represents. Since one radian is approximately 57.3 degrees, 30 radians equals about 1719 degrees, which is almost 5 complete rotations around the circle. At this position, the sine value is approximately negative 0.988, which is nowhere near 0.5. In summary, the root cause of Molly's error is confusing the numerical value of an angle measured in degrees with its value in radians. While 30 degrees correctly gives sine equals one half, 30 radians is a completely different angle that gives sine approximately negative 0.988. The correct answer in radians is pi over 6, which is approximately 0.524 radians. In conclusion, Molly is incorrect. The root cause is confusing degrees with radians. When sine theta equals one half, theta equals 30 degrees, which converts to pi over 6 radians, approximately 0.524 radians. Molly mistakenly used 30 radians instead of converting the degree measure. This highlights the critical importance of always checking and converting units properly in mathematics.