Exam 8: The Unit Circle and Functions of Trigonometry

Find the angle of smallest positive measure coterminal with $-418^{\circ}$ .

graph the given function over a two-period interval. Identify asymptotes when applicable. -The average monthly high temperature $\left(\right.$ in $\mathrm{F}^{\circ}$ ) in London can be modeled using the trigonometric function defined by $f(x)=14 \sin \left[\frac{\pi}{6}(x-4.2)\right]+57$ , where $x$ is the month and $x=1$ corresponds to January. (a) Graph $f$ over the interval $1 \leq x \leq 25$ . (b) Determine the amplitude, period, phase shift, and vertical translation of $f$ . (c) What is the average monthly high temperature for the month of October? (d) Find the maximum and minimum average monthly high temperatures and the months when they occur. (e) What would be an approximation for the average yearly high temperature in London? How is this related to the vertical translation of the sine function in the formula for $f$ ?

Find the exact values of each part labeled with a letter.

Solve the triangle.

the formula $s(t)=-4 \cos 3 t$ gives the height (in inches) of a weight attached to a spring after $t$ seconds -Find the maximum height that the weight rises above the equilibrium position of $y=0$ .

Find the exact value of $\sec \left(585^{\circ}\right)$ .

the formula $s(t)=-9 \cos \frac{\pi}{2} t$ gives the height (in inches) of a weight attached to a spring after $t$ seconds. -When does the weight reach its maximum height if $t \geq 0$ ?

Find the length of an arc intercepted by an angle of $120^{\circ}$ in a circle with radius 7 inches.