Trigonometry Vocabulary Flashcards

Questions and Answers

What is the measurement of triangles called?

Geometry

Trigonometry (correct)

Calculus

Algebra

What is defined as a measurement determined by rotating a ray about its endpoint?

Angle

What do you call the starting position of the ray?

Initial Side

What is the term for the position after rotation of the ray?

Terminal Side Signup and view all the answers

What is the endpoint of the ray called?

Vertex Signup and view all the answers

What is the position of an angle on a coordinate system in which the origin is the vertex and the initial side coincides with the positive x-axis called?

Standard position Signup and view all the answers

What is generally defined as an angle that is counterclockwise?

Positive angles Signup and view all the answers

What do you call angles that are generally clockwise?

Negative angles Signup and view all the answers

What are angles that have the same initial side and terminal side called?

Coterminal Signup and view all the answers

What determines the measure of an angle?

Amount of rotation from the initial side to the terminal side Signup and view all the answers

What is an angle whose vertex is the center of the circle called?

Central angle Signup and view all the answers

What is another form of measuring angles, which is the measure of central angle X that intercepts an arc S equal in length to the radius R of the circle?

Radian Signup and view all the answers

What is an angle less than 90 degrees called?

Acute Signup and view all the answers

What is an angle greater than 90 degrees and less than 180 degrees called?

Obtuse Signup and view all the answers

What do you call angles that equal 90 degrees?

Complementary Signup and view all the answers

What are angles whose sum is equal to 180 degrees called?

Supplementary Signup and view all the answers

What is a way to measure an angle?

Degree Signup and view all the answers

What is the path distance moved per unit of time along a circular arc called?

Linear speed Signup and view all the answers

What is the rate at which a body rotates about an axis, usually expressed in radians per second?

Angular speed Signup and view all the answers

What is a circle where the radius equals one called?

Unit circle Signup and view all the answers

What is the trigonometric function that equals the y coordinate?

Sine Signup and view all the answers

What is the trigonometric function that equals the x coordinate?

Cosine Signup and view all the answers

What is the trigonometric function that equals y/x coordinate?

Tangent Signup and view all the answers

What is the trigonometric function that equals 1/y coordinate?

Cosecant Signup and view all the answers

What is the trigonometric function that equals 1/x coordinate?

Secant Signup and view all the answers

What is the trigonometric function that equals x/y coordinate?

Cotangent Signup and view all the answers

What are functions that behave in a repetitive manner called?

Periodic Signup and view all the answers

What is the smallest number which is periodic called?

Period Signup and view all the answers

What do you call the side opposite of the 90 degree angle?

Hypotenuse Signup and view all the answers

What is the side opposite of the theta called?

Opposite side Signup and view all the answers

What is the side closest to the theta called?

Adjacent side Signup and view all the answers

What represents the angle from the horizontal upward to an angle?

Angle of elevation Signup and view all the answers

What are the objects that lie below the horizontal called?

Angle of depression Signup and view all the answers

What are the values of the trigonometric functions of angles greater than 90 degrees determined from?

Corresponding acute angles Signup and view all the answers

What is the graph of the sine function called?

Sine curve Signup and view all the answers

What is defined as one period of the function?

One cycle Signup and view all the answers

What are the intercepts, maximum points, and minimum points called?

Key points Signup and view all the answers

What is the absolute value of a called?

Amplitude Signup and view all the answers

What is defined as the exact opposite of the first wave?

Reflection Signup and view all the answers

What is the number added to x called?

Phase shift Signup and view all the answers

What is the inverse sine function represented as?

Y=sin^-1 x Signup and view all the answers

What is the inverse cosine function represented as?

Y=cos^-1 x Signup and view all the answers

What is the inverse tangent function interval?

(-pi/2, pi/2) Signup and view all the answers

What is the direction in surveying and navigation called?

Bearings Signup and view all the answers

What describes the motion of a wave described by a sine or cosine function?

Simple harmonic motion Signup and view all the answers

Study Notes

Trigonometry Fundamentals

Trigonometry involves the measurement of triangles.
Angles are determined by the rotation of a ray around its endpoint, creating an initial and terminal side.
The vertex of an angle is the endpoint of the ray.

Angle Positions

Standard position refers to placing an angle so its vertex is at the origin with the initial side along the positive x-axis.
Positive angles rotate counterclockwise, while negative angles rotate clockwise.

Types of Angles

Angles sharing the same initial and terminal sides are called coterminal.
The measure of an angle is the rotation from the initial to the terminal side.
Central angles have their vertex at the center of a circle.
Radians provide an alternative angle measurement, defined as the central angle intercepting an arc equal in length to the circle's radius.

Angle Classifications

Acute angles are less than 90 degrees.
Obtuse angles range from greater than 90 degrees to less than 180 degrees.
Complementary angles sum to 90 degrees, while supplementary angles add up to 180 degrees.
Angles are measured in degrees, with 360 degrees completing a full rotation.

Motion and Speed in Trigonometry

Linear speed refers to the distance traveled along a circular arc per time unit.
Angular speed describes the rate of rotation around an axis, expressed in radians per second.

Trigonometric Functions

The unit circle has a radius of one, useful for deriving trigonometric functions.
Sine corresponds to the y-coordinate, cosine to the x-coordinate, and tangent equals y/x.
Cosecant, secant, and cotangent are the reciprocals of sine, cosine, and tangent, respectively.

Function Characteristics

Periodic functions repeat values in a regular cycle, characterized by their period (smallest repeating interval).
The hypotenuse is the side opposite the right angle in a triangle.
The opposite side is opposite the angle in question, while the adjacent side is next to it.

Angle Measurements

The angle of elevation rises from the horizontal upward, while the angle of depression descends below the horizontal.
Reference angles help determine the values of trigonometric functions for angles greater than 90 degrees using corresponding acute angles.

Graphs and Transformations

The sine curve represents the graphical depiction of the sine function.
One cycle of a function contains all key points, which include intercepts, maximum, and minimum points.
Amplitude measures the height of waves, while phase shifts adjust the function horizontally.
Reflection creates a wave that mirrors the original.

Inverse Trigonometric Functions

Inverse sine, cosine, and tangent functions offer ways to find angles from given sine, cosine, and tangent values, with specified domains and ranges.

Practical Applications

Bearings indicate direction in navigation and surveying.
Simple harmonic motion describes wave patterns modeled by sine or cosine functions.

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Description

Test your understanding of key trigonometry terms with these flashcards. Each card provides a word along with its definition to help reinforce your knowledge of angles, rays, and triangles. Perfect for students learning trigonometry concepts.