Activity 4.4.2.
For each of the following different scenarios, draw a picture of the situation and use inverse trigonometric functions appropriately to determine the missing information both exactly and approximately.
(a)
Consider a right triangle with legs of length \(11\) and \(13\text{.}\) What are the measures (in radians) of the non-right angles and what is the length of the hypotenuse?
(b)
Consider an angle \(\alpha\) in standard position (vertex at the origin, one side on the positive \(x\)-axis) for which we know \(\cos(\alpha) = -\frac{1}{2}\) and \(\alpha\) lies in quadrant III. What is the measure of \(\alpha\) in radians? In addition, what is the value of \(\sin(\alpha)\text{?}\)
(c)
Consider an angle \(\beta\) in standard position for which we know \(\sin(\beta) = 0.1\) and \(\beta\) lies in quadrant II. What is the measure of \(\beta\) in radians? In addition, what is the value of \(\cos(\beta)\text{?}\)
