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Questions and Answers
What is the measurement of triangles called?
What is the measurement of triangles called?
What is defined as a measurement determined by rotating a ray about its endpoint?
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?
What do you call the starting position of the ray?
Initial Side
What is the term for the position after rotation of the ray?
What is the term for the position after rotation of the ray?
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What is the endpoint of the ray called?
What is the endpoint of the ray called?
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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?
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?
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What is generally defined as an angle that is counterclockwise?
What is generally defined as an angle that is counterclockwise?
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What do you call angles that are generally clockwise?
What do you call angles that are generally clockwise?
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What are angles that have the same initial side and terminal side called?
What are angles that have the same initial side and terminal side called?
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What determines the measure of an angle?
What determines the measure of an angle?
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What is an angle whose vertex is the center of the circle called?
What is an angle whose vertex is the center of the circle called?
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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?
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?
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What is an angle less than 90 degrees called?
What is an angle less than 90 degrees called?
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What is an angle greater than 90 degrees and less than 180 degrees called?
What is an angle greater than 90 degrees and less than 180 degrees called?
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What do you call angles that equal 90 degrees?
What do you call angles that equal 90 degrees?
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What are angles whose sum is equal to 180 degrees called?
What are angles whose sum is equal to 180 degrees called?
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What is a way to measure an angle?
What is a way to measure an angle?
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What is the path distance moved per unit of time along a circular arc called?
What is the path distance moved per unit of time along a circular arc called?
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What is the rate at which a body rotates about an axis, usually expressed in radians per second?
What is the rate at which a body rotates about an axis, usually expressed in radians per second?
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What is a circle where the radius equals one called?
What is a circle where the radius equals one called?
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What is the trigonometric function that equals the y coordinate?
What is the trigonometric function that equals the y coordinate?
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What is the trigonometric function that equals the x coordinate?
What is the trigonometric function that equals the x coordinate?
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What is the trigonometric function that equals y/x coordinate?
What is the trigonometric function that equals y/x coordinate?
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What is the trigonometric function that equals 1/y coordinate?
What is the trigonometric function that equals 1/y coordinate?
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What is the trigonometric function that equals 1/x coordinate?
What is the trigonometric function that equals 1/x coordinate?
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What is the trigonometric function that equals x/y coordinate?
What is the trigonometric function that equals x/y coordinate?
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What are functions that behave in a repetitive manner called?
What are functions that behave in a repetitive manner called?
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What is the smallest number which is periodic called?
What is the smallest number which is periodic called?
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What do you call the side opposite of the 90 degree angle?
What do you call the side opposite of the 90 degree angle?
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What is the side opposite of the theta called?
What is the side opposite of the theta called?
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What is the side closest to the theta called?
What is the side closest to the theta called?
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What represents the angle from the horizontal upward to an angle?
What represents the angle from the horizontal upward to an angle?
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What are the objects that lie below the horizontal called?
What are the objects that lie below the horizontal called?
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What are the values of the trigonometric functions of angles greater than 90 degrees determined from?
What are the values of the trigonometric functions of angles greater than 90 degrees determined from?
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What is the graph of the sine function called?
What is the graph of the sine function called?
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What is defined as one period of the function?
What is defined as one period of the function?
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What are the intercepts, maximum points, and minimum points called?
What are the intercepts, maximum points, and minimum points called?
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What is the absolute value of a called?
What is the absolute value of a called?
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What is defined as the exact opposite of the first wave?
What is defined as the exact opposite of the first wave?
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What is the number added to x called?
What is the number added to x called?
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What is the inverse sine function represented as?
What is the inverse sine function represented as?
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What is the inverse cosine function represented as?
What is the inverse cosine function represented as?
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What is the inverse tangent function interval?
What is the inverse tangent function interval?
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What is the direction in surveying and navigation called?
What is the direction in surveying and navigation called?
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What describes the motion of a wave described by a sine or cosine function?
What describes the motion of a wave described by a sine or cosine function?
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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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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.
