91Ó°ÊÓ

Use a calculator in radian mode to approximate the functional value. $$\cos ^{-1} .76$$

Use a calculator in radian mode to approximate the functional value. $$\sin ^{-1}(\sin 7)[\text { The answer is not } 7 .]$$

Use a calculator in radian mode to approximate the functional value. $$\cos ^{-1}(\cos 3.5)$$

Suppose that another model plane is flying while attached to the ground by a 100 foot long wire that is always kept taut. Let \(h\) denote the height of the plane above the ground and \(\theta\) the radian measure of the angle the wire makes with the ground. (The figure for Exercise 65 is the case when \(x=\) \(100 \text { and } h=40 .)\) (a) Express \(\theta\) as a function of the height \(h\) (b) What is \(\theta\) when the plane is 55 feet above the ground? (c) When \(\theta=1\) radian, how high is the plane?

Show that the restricted cotangent function, whose domain is the interval \((0, \pi),\) has an inverse function. Sketch its graph.

The number of hours of daylight in Detroit on day \(t\) of a non-leap year (with \(t=0\) being January 1 ) is given by the function $$d(t)=3 \sin \left[\frac{2 \pi}{365}(t-80)\right]+12$$ (a) On what days of the year are there exactly 11 hours of daylight? (b) What day has the maximum amount of daylight?