Problems

01

Solve trig equation using trig identities

Find all values of $x\in [0,2\pi ]$ such that $\sin 2x=\sin x$.

(Hint: double angle formula.)

02

Related rates - balloon volume and radius

Suppose a balloon maintains a spherical shape while it is inflated. Suppose its radius is increasing at a rate of $4cm/s$.

• (a) Write the balloon’s radius as a function of time $t$.
• (b) Write the balloon’s volume as a function of time $t$.

Interpret your answer.

03

Determining exponential parameters from points on graph

Find the constant parameters $C$ and $b$ for which the exponential function $f(x)=C{b}^x$ has the following graph:

04

Exact secant

What is $\sec (\frac{7\pi }{4})$? (Give an exact answer.)

05

Function formula from modifying a graph

The function $f(x)=\sqrt{x(6-x)}$ has the first graph below. What function has the second graph?

06

Transforming a graph

Graph the function $f(x)=5\sqrt{x+5}$ by first graphing $g(x)=\sqrt{x}$ and appropriately transforming this graph.