The graph of $y=\cos (x)$ reaches a minimum value of $-1$ at $x=\pi$. What does the graph of $y=\sec (x)$ do at $x=\pi$?

In triangle $UVW$ the sides opposite angles $U$ and $W$ are known, along with angle $V$, which lies between them. Which equation gives the remaining side?

Write $12\left(\cos 240^{\circ }+i\sin 240^{\circ }\right)$ in the form $a+bi$, with exact values.

Describe the end behavior of $g(x)=\frac{2x^2-x}{3x+5}$.

For an acute angle $\theta$ in a right triangle, $\sin \theta =\frac{8}{17}$. What is $\cos \theta$?

What is the value of $\left(\genfrac{}{}{0ex}{}{10}{2}\right)$?

A vector runs from the point $(-4,-2)$ to the point $(-14,22)$. Find its magnitude.

What does the graph of $s(x)=\frac{(x+1)(x+6)}{(x+1)(x+5)}$ do at each of its excluded inputs?

Which system does the augmented matrix $\left[\begin{array}{cccc}-3& 0& 4& -2\\ -8& -4& 0& -1\end{array}\right]$ represent?

In triangle $ABC$, angle $A$ measures 38 degrees, the side opposite it measures $18$, and the side opposite angle $B$ measures $12$. How many triangles fit these measurements?

In the expansion of $(x+2{)}^7$ written in descending powers of $x$, what is the fifth term?

At which zero does the graph of $v(x)=(x+1{)}^2(x-4)(x-5{)}^3$ touch the $x$-axis and turn back without crossing?

Which row operation turns the first entry of the second row of $\left[\begin{array}{ccc}1& 5& 3\\ 5& 2& -2\end{array}\right]$ into $0$?

A rope pulls a crate along the ground with a force of 120 pounds, and the rope makes an angle of 30 degrees above the horizontal. Which expression gives the HORIZONTAL component of that force?

Find every solution of $\sin \theta =\frac{\sqrt{2}}{2}$ for $0^{\circ }\le \theta <360^{\circ }$.

Apply a sum or difference identity to $\cos \left(\frac{3\pi }{2}-x\right)$ and simplify the result.

Which expression is equivalent to $\frac{\sec \theta }{\csc \theta }$?

Find every solution of $\cos 2x=\cos x$ on the interval $\left[0,2\pi \right)$.

The graph of $g$ passes through $(-3,-2)$ and $(-1,4)$. Find the slope of the secant line joining those two points.

Write $4x^2-25y^2-40x=0$ in standard form.

Which expression is a correct half-angle form for $\tan \frac{\alpha }{2}$?

Which line is a vertical asymptote of $y=\cot \left(2\left(x-\frac{\pi }{2}\right)\right)$?

Evaluate ${\lim }_{h\to 0}\frac{\frac{1}{7+h}-\frac{1}{7}}{h}$.

Which statement about $\mathbf{u}=⟨0,-7⟩$ and $\mathbf{v}=⟨5,6⟩$ is correct?

For $f(x)=4x^2+2x$, the average rate of change over $\left[-2,b\right]$ is $-10$. Find $b$.

Use a double-angle identity to find the exact value of $1-2{\sin }^{2}90^{\circ }$.

Use a half-angle identity to find the exact value of $\cos 67.5^{\circ }$ in simplest radical form.

In triangle $XYZ$, angle $X$ measures 66 degrees, angle $Z$ measures 32 degrees, and the side opposite angle $Z$ measures $30$. What is the measure of angle $Y$?

On which interval of the form $\left[a,\infty \right)$, with the smallest possible $a$, is $k(x)=x^2+6x+11$ one-to-one?

A curve is given by $x=t^2-5$ and $y=-3t-2$. Which point does the curve pass through at $t=-3$?

Over five equally spaced readings, a colony of bacteria measures 10, 11, 12, 13 and 14 thousands of cells, one reading per hour. Which model reproduces the record?

In triangle $PQR$, the side opposite angle $P$ measures $9$, the side opposite angle $Q$ measures $10$, and the side opposite angle $R$ measures $18$. Which value is closest to the measure of angle $R$?

What does direct substitution give for ${\lim }_{x\to -1}\frac{x^2+6x-7}{x^2-1}$, and what follows from it?

Which system does the augmented matrix $\left[\begin{array}{cccc}2& 0& -3& -4\\ 2& -1& 0& -12\end{array}\right]$ represent?

Apply a double-angle identity to write $\cos 4x$ using the cosine of $2x$ alone. Which expression results?

In the expansion of $(x+2{)}^8$ written in descending powers of $x$, what is the third term?

A projectile's position in feet after $t$ seconds is $x=20t$ and $y=-16t^2+64t$. Where is it at $t=3$ seconds?

What is the range of $y=2\csc (x)$?

Over five equally spaced readings, a savings balance measures 6, 5, 4, 3 and 2 dollars, one reading per year. Which model reproduces the record?

Solve $3{\left(2\right)}^x=48$ for $x$.

What is the midline of $y=-5\sin (3x)+2$?

A rocket has height $y=-16t^2+80t$ feet after $t$ seconds, with $x=60t$ feet of horizontal travel. At what time does it return to the ground?

Taken from the first point to the second, which pair of points gives the vector $⟨5,-8⟩$?

What is the midline of $y=-3\cos (x)+1$?

Find every solution of $2\cos x-\sqrt{3}=0$ on the interval $\left[0,2\pi \right)$.

Let $\mathbf{r}=⟨3,-2⟩$ and $\mathbf{s}=⟨-3,8⟩$. Find $\mathbf{r}\cdot \mathbf{s}$.

A vector has initial point $(-3,6)$ and terminal point $(5,8)$. Write the vector in component form.

A semi-log plot of $\log y$ against $x$ is a straight line with slope $1$ passing through $(0,2)$. Which model does that recover?

Write $x^2+y^2=6y$ as a polar equation.

What is the range of $y=2\arcsin (x)$?

Which statement about $\mathbf{u}=⟨6,-1⟩$ and $\mathbf{v}=⟨4,4⟩$ is correct?

Solve $x^3-x>0$ and write the solution in interval notation.

A system in $x$, $y$ and $z$ row reduces to $\left[\begin{array}{cccc}1& 0& 4& -3\\ 0& 1& -4& 6\\ 0& 0& 0& 6\end{array}\right]$. What does this tell you about the system?

Find the inverse of $f(x)=3e^{4x}+5$.

How does the graph of $y=\tan (4x)$ differ from the graph of $y=\tan (x)$?

Which curve does $r=6\sin (3\theta )$ trace?

Eliminate the parameter from $x=2t$ and $y=t^2+5$ to write a single equation in $x$ and $y$.

At which value of $x$ does $w(x)=\frac{(x-9)(x-1)}{(x-9)(x+9)}$ have an INFINITE discontinuity?

The repeating decimal $0.\overline{45}$ is the sum of an infinite geometric series whose first term is $\frac{45}{100}$. What fraction does it equal, in lowest terms?

What is the modulus of $z=-3-4i$?

Evaluate $\arcsin \left(-1\right)$ in radians.

Convert the polar point $\left(8,\frac{5\pi }{3}\right)$ to rectangular coordinates, in exact form.

Eliminate the parameter from $x=3t$ and $y=t^2-1$ to write a single equation in $x$ and $y$.

A circle has radius $12$ inches and a central angle measuring 60 degrees. What is the exact area of the sector?

Find the inverse of $f(x)=4e^{3x}-6$.

Use De Moivre's theorem to find ${\left[5\left(\cos 110^{\circ }+i\sin 110^{\circ }\right)\right]}^3$ in trigonometric form, with the argument on $\left[0^{\circ },360^{\circ }\right)$.

A circle has radius $8$ inches and a central angle measuring $\frac{2\pi }{5}$ radians. What is the exact area of the sector?

Solve $4{\left(3\right)}^x=324$ for $x$.

From a point $52$ m above sea level at the top of a cliff, the angle of depression to a kayak is 50 degrees. Which value is closest to the horizontal distance from the base to a kayak?

A function is defined by $s(x)=x^2$ for $x\le 5$ and by $s(x)=-x+30$ for $x>5$. Is $s$ continuous at $x=5$?

Simplify $\frac{g(x+h)-g(x)}{h}$ for $g(x)=-2x^2+9x$.

Solve $(x+4)(x+3)>0$ and write the solution in interval notation.

A table gives $h(-3)=-28$, $h(-2)=-5$, $h(-1)=0$, $h(0)=5$ and $h(1)=28$. Between which inputs does the graph change from concave down to concave up?

Find the sum of the infinite series $27+21+\frac{49}{3}+\frac{343}{27}+\cdots$.

At which zero does the graph of $w(x)=(x+4{)}^2(x+8)(x+7{)}^3$ touch the $x$-axis and turn back without crossing?

Find every solution of $2{\sin }^{2}x-\sin x=0$ on the interval $\left[0,2\pi \right)$.

How many petals does the graph of $r=7\cos (3\theta )$ have, and how far does each reach from the pole?

In a right triangle one acute angle measures 55 degrees, and the hypotenuse measures $30$. Which value is closest to the length of the leg opposite that angle?

Given that $\sin \theta =\frac{7}{25}$ and $\theta$ lies in the second quadrant, find $\cos \theta$.

Solve ${\log }_{2}x=4$ for $x$.