### Key Terms

- adjacent side
- in a right triangle, the side between a given angle and the right angle

- angle
- the union of two rays having a common endpoint

- angle of depression
- the angle between the horizontal and the line from the object to the observer’s eye, assuming the object is positioned lower than the observer

- angle of elevation
- the angle between the horizontal and the line from the object to the observer’s eye, assuming the object is positioned higher than the observer

- angular speed
- the angle through which a rotating object travels in a unit of time

- arc length
- the length of the curve formed by an arc

- area of a sector
- area of a portion of a circle bordered by two radii and the intercepted arc; the fraction $\frac{\theta}{2\pi}.$ multiplied by the area of the entire circle

- cosecant
- the reciprocal of the sine function: on the unit circle, $\text{csc}\phantom{\rule{0.3em}{0ex}}t=\frac{1}{y},y\ne 0$

- cosine function
- the
*x*-value of the point on a unit circle corresponding to a given angle

- cotangent
- the reciprocal of the tangent function: on the unit circle, $\text{cot}\phantom{\rule{0.3em}{0ex}}t=\frac{x}{y},y\ne 0$

- coterminal angles
- description of positive and negative angles in standard position sharing the same terminal side

- degree
- a unit of measure describing the size of an angle as one-360th of a full revolution of a circle

- hypotenuse
- the side of a right triangle opposite the right angle

- identities
- statements that are true for all values of the input on which they are defined

- initial side
- the side of an angle from which rotation begins

- linear speed
- the distance along a straight path a rotating object travels in a unit of time; determined by the arc length

- measure of an angle
- the amount of rotation from the initial side to the terminal side

- negative angle
- description of an angle measured clockwise from the positive
*x*-axis

- opposite side
- in a right triangle, the side most distant from a given angle

- period
- the smallest interval $P$ of a repeating function $f$ such that $f(x+P)=f(x)$

- positive angle
- description of an angle measured counterclockwise from the positive
*x*-axis

- Pythagorean Identity
- a corollary of the Pythagorean Theorem stating that the square of the cosine of a given angle plus the square of the sine of that angle equals 1

- quadrantal angle
- an angle whose terminal side lies on an axis

- radian
- the measure of a central angle of a circle that intercepts an arc equal in length to the radius of that circle

- radian measure
- the ratio of the arc length formed by an angle divided by the radius of the circle

- ray
- one point on a line and all points extending in one direction from that point; one side of an angle

- reference angle
- the measure of the acute angle formed by the terminal side of the angle and the horizontal axis

- secant
- the reciprocal of the cosine function: on the unit circle, $\mathrm{sec}\phantom{\rule{0.3em}{0ex}}t=\frac{1}{x},x\ne 0$

- sine function
- the
*y*-value of the point on a unit circle corresponding to a given angle

- standard position
- the position of an angle having the vertex at the origin and the initial side along the positive
*x*-axis

- tangent
- the quotient of the sine and cosine: on the unit circle, $\mathrm{tan}\phantom{\rule{0.3em}{0ex}}t=\frac{y}{x},x\ne 0$

- terminal side
- the side of an angle at which rotation ends

- unit circle
- a circle with a center at $(0,0)$ and radius 1

- vertex
- the common endpoint of two rays that form an angle