$\tan \theta$ is the reciprocal of which function?

What is the midline of $y=5\cos (4x)-1$?

A tangent graph has consecutive vertical asymptotes at $x=-\frac{\pi }{8}$ and $x=\frac{\pi }{8}$, passes through the origin, and falls from large positive values down to large negative values between those two asymptotes. Which equation fits it?

Which line is a vertical asymptote of $y=\sec \left(4\left(x-\frac{\pi }{2}\right)\right)$?

In right triangle $PQR$ the right angle is at $R$. The leg adjacent to angle $P$ measures $9$ and the leg opposite it measures $20$. Which value is closest to the measure of angle $P$?

What is the period of $y=3\cos (3x)+4$?

For an acute angle $\theta$ in a right triangle, $\tan \theta =\frac{3}{4}$. What is $\sin \theta$?

Find every solution of $2{\sin }^{2}x-\cos x-1=0$ on the interval $\left[0,2\pi \right)$.

A surveyor knows one acute angle $\theta$ of a right triangle and the hypotenuse $h$, and wants the length $x$ of the leg that touches the known angle. Which equation gives $x$ in a single step?

In triangle $RST$, the side opposite angle $R$ measures $13$, the side opposite angle $S$ measures $6$, and the side opposite angle $T$ measures $10$. Which value is closest to the measure of angle $T$?

One inverse trigonometric function has the range $\left(-\frac{\pi }{2},\frac{\pi }{2}\right)$, open at both ends. Which function is it?

Convert the polar point $\left(8,\frac{2\pi }{3}\right)$ to rectangular coordinates, in exact form.

Find the unit vector in the direction of $\mathbf{w}=⟨24,10⟩$.

The graph of $y=\arcsin (x)$ is the reflection across the line $y=x$ of which curve?

Find every solution of $2\sin x-1=0$ on the interval $\left[0,2\pi \right)$.

What is the period of $y=\sec \left(5x\right)$?

From a control tower window $120$ m above the ground, the angle of depression to a parked aircraft is 20 degrees. Which value is closest to the horizontal distance from the base of the tower to the aircraft?

What is the period of $y=-4\cos (4x)+2$?

Which statement about $\mathbf{u}=⟨5,-5⟩$ and $\mathbf{v}=⟨-2,6⟩$ is correct?

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

In triangle $ABC$, angle $A$ measures 57 degrees, angle $C$ measures 79 degrees, and the side between them measures $30$. Which value is closest to the side opposite angle $A$?

In right triangle $PQR$ the right angle is at $R$. The leg opposite angle $Q$ measures $12$ and the hypotenuse measures $13$. What is $\sec Q$?

Which statement about $\mathbf{u}=⟨-4,-5⟩$ and $\mathbf{v}=⟨-6,6⟩$ is correct?

What is the period of $y=\sin (6x)-5$?

In triangle $RST$ the measurements given are two angles and a side not between them. Which relation do those parts support, and why?

A circle has radius $4$ m and a central angle measuring $\frac{\pi }{2}$ radians. What is the exact area of the sector?

How many petals does the graph of $r=5\cos (4\theta )$ have, and how far does each reach from the pole?

In triangle $DEF$, angle $D$ measures 51 degrees, the side opposite it measures $4$, and the side opposite angle $E$ measures $10$. How many triangles fit these measurements?

What is the period of $y=-\cos (3x)-3$?

In triangle $PQR$, angle $P$ measures 72 degrees, angle $R$ measures 66 degrees, and the side between them measures $30$. Which value is closest to the side opposite angle $P$?

Find every solution of ${\sin }^{2}x+3\sin x=0$ on the interval $\left[0,2\pi \right)$.

What is the period of $y=3\tan \left(5x\right)$?

What is the domain of $y=\arctan \left(3x-2\right)$?

Simplify ${\tan }^2\theta -{\sec }^2\theta$.

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

Between two consecutive vertical asymptotes, how does the graph of $y=\cot (x)$ behave?

Evaluate $\arccos \left(0\right)$ in radians.

In triangle $UVW$, angle $U$ measures 51 degrees, the side opposite it measures $17$, and the side opposite angle $V$ measures $20$. Taking the solution in which angle $V$ is obtuse and measures about 113.9 degrees, which value is closest to the side opposite angle $W$?

What is the period of $y=-\cos (4x)-3$?

Two radio masts stand $400$ km apart on a straight highway. From the line joining them, the angle to the stranded vehicle is 57 degrees at the first and 72 degrees at the second. Which is closest to the distance from the first to the stranded vehicle?

Evaluate $\arctan \left(-\sqrt{3}\right)$ in radians.

Describe the graph of $r=10\cos \theta$.

In triangle $RST$, angle $R$ measures 29 degrees, angle $S$ measures 68 degrees, and the side opposite angle $R$ measures $12$. Which value is closest to the side opposite angle $S$?

How many solutions does the equation $\sin x=\frac{1}{3}$ have on the interval $\left[0,6\pi \right)$?

What is the modulus of $z=-12+9i$?

Which single trigonometric value is equal to ${\cos }^{2}65^{\circ }-{\sin }^{2}65^{\circ }$?

Let $\mathbf{m}=⟨3,3⟩$ and $\mathbf{n}=⟨2,-1⟩$. Find $\mathbf{m}-\mathbf{n}$.

What is the amplitude of $y=-6\sin (3x)-4$?

Write the rectangular point $(-1,\sqrt{3})$ in polar form with $r>0$ and $0\le \theta <2\pi$.

A triangle has two sides measuring $19$ m and $9$ m, and the angle between them measures 68 degrees. Which value is closest to the area of the triangle?

What is the period of $y=-\tan \left(4x\right)$?

In triangle $ABC$, angle $A$ measures 70 degrees, angle $C$ measures 46 degrees, and the side opposite angle $C$ measures $24$. What is the measure of angle $B$?

Simplify $\frac{\left(\sec \theta -\csc \theta \right)\left(\sec \theta +\csc \theta \right)}{\sec \theta -\csc \theta }$.

A lawn sprinkler sprays water $12$ m and turns through a central angle measuring $\frac{3\pi }{4}$ radians. What is the exact area of the lawn it waters?

Write $\cos \left(\arctan (x)\right)$ as an algebraic expression in $x$.

Let $\mathbf{a}=⟨-6,8⟩$ and $\mathbf{b}=⟨3,3⟩$. Find $\mathbf{a}+\mathbf{b}$.

Evaluate $\arccos \left(-\frac{\sqrt{3}}{2}\right)$, giving the answer in degrees.

Simplify $1-{\sin }^2\theta$.

What is the midline of $y=-3\sin (x)-4$?

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