Trigonometry Midterm Review

This set of vocabulary flashcards covers essential trigonometric terms, identities, and formulas derived from the midterm review notes, including angle properties, unit circle functions, and periodic graph characteristics.

Supplementary Angles

Two angles whose measures have a sum of $180^{\circ}$.

Coterminal Angles

Angles in standard position that have the same terminal side, found by adding or subtracting multiples of $360^{\circ}$ or $2\pi$ radians.

Standard Position

An angle positioned with its vertex at the origin and its initial side along the positive x-axis.

Cosecant ($\csc \theta$)

The reciprocal of the sine function, defined as $\frac{r}{y}$ or $\frac{1}{\sin \theta}$.

Secant ($\sec \theta$)

The reciprocal of the cosine function, defined as $\frac{r}{x}$ or $\frac{1}{\cos \theta}$.

Cotangent ($\cot \theta$)

The reciprocal of the tangent function, defined as $\frac{x}{y}$ or $\frac{1}{\tan \theta}$.

Cofunction

A trigonometric function whose value for an acute angle $\theta$ is equal to the value of its corresponding function at the complement of $\theta$ (e.g., $\cot(28.1^{\circ}) = \tan(90^{\circ} - 28.1^{\circ})$).

Reference Angle

The acute angle formed by the terminal side of an angle and the x-axis.

Radian Conversion

The process of converting degrees to radians by multiplying the degree measure by $\frac{\pi}{180^{\circ}}$.

Area of a Sector

The region bounded by a central angle and its intercepted arc, calculated using the formula $A = \frac{1}{2}r^2\theta$, where $\theta$ must be in radians.

Arc Length ($s$)

The distance along the curved line of a circle, calculated as $s = r\theta$, where $\theta$ is in radians.

Amplitude

The maximum displacement from the equilibrium position (midline) of a periodic function, given by $|a|$ in the form $y = a \sin bx$ or $y = a \cos bx$.

Period

The horizontal length of one complete cycle of a periodic function, calculated as $\frac{2\pi}{b}$ for sine and cosine functions.

Phase Shift

The horizontal translation of a trigonometric function's graph.

Vertical Translation

A vertical shift of a function's graph, represented by the constant added or subtracted from the function (e.g., the $-4$ in $y = -4 + 3 \sin 4x$).

Angular Speed ($\omega$)

The rate at which a central angle changes over time, calculated as $\omega = \frac{\theta}{t}$.

Linear Speed ($v$)

The rate at which a point on the edge of a circle moves, calculated as $v = r\omega$.

Frequency

The number of cycles a periodic system completes per unit of time, defined as the reciprocal of the period ($\frac{1}{\text{period}}$).