Precalculus Transformations Quiz and Flashcards

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Questions and Answers

What is the main focus of the precalculus course at Nevada State College?

What is Bloom's Taxonomy used for in the context of the precalculus course?

Why is it important to use radians rather than degrees in mathematics?

Degrees are not accurate
Radians have a geometric significance (correct)
Degrees are difficult to understand
Radians are easier to memorize

What is the unit circle and why is it crucial for trigonometric functions?

How do angles get measured in precalculus?

Why do trigonometric functions have periodicity with a period of 2π?

What is the relationship between positive and negative angles in trigonometric functions on the unit circle?

What does the Pythagorean theorem state about right triangles?

Why are reciprocal identities, quotient identities, and Pythagorean identities important in trigonometry?

What do reference angles in all four quadrants help determine in trigonometry?

What defines the repetition within regular intervals for a function?

What does the amplitude of a function measure?

Flashcards

Trigonometry

Bloom's Taxonomy

Definition of Angles

Angle Measurement

Unit Circle

Special Angles

Periodicity

Pythagorean theorem

Special Right Triangles

Trigonometric Identities

Amplitude

Transformation Order

Study Notes

The precalculus course at Nevada State College focuses on trigonometry, which is the study of triangles and their connections to circles.
Bloom's Taxonomy is used to gauge the depth of learning, ranging from basic information recall to advanced idea generation.
The course structure includes pre-class activities, in-class learning activities, and homework to build a comprehensive understanding of the topics.
Math learning is emphasized as a process of connecting ideas and applying concepts rather than just memorizing rules.
Angles are defined based on the intersection of line segments, with terms like vertex, initial side, and terminal side determining measurement direction.
Angles can be measured in degrees or radians, with radians being preferred in mathematics due to their geometric significance.
The unit circle, a circle with radius 1 centered at the origin, is crucial for understanding trigonometric functions.
Special angles on the unit circle, like 0, π/2, π, 3π/2, and 2π, have specific coordinates used to calculate trigonometric functions.
Trigonometric functions have periodicity (repetition at regular intervals) with a period of 2π due to the circular nature of the unit circle.
Symmetry in trigonometric functions is observed through the relationship between positive and negative angles on the unit circle, impacting functions like sine, cosine, secant, and cosecant.- Trigonometry can be understood through right triangles where the two legs and the hypotenuse are defined, along with the relationships between them based on an angle.
The Pythagorean theorem states that a² + b² = c² for right triangles, allowing to find the length of the third side if two sides are known.
All six trigonometric functions (sine, cosine, tangent, cosecant, secant, cotangent) can be defined in terms of the relationships between sides of right triangles.
Special right triangles (45-45-90 and 30-60-90) provide specific side lengths and values for trigonometric functions (sine, cosine, tangent) that are used in the unit circle.
Reciprocal identities, quotient identities, and Pythagorean identities are important in trigonometry for deriving relationships between trigonometric functions.
Understanding signs of trigonometric functions in different quadrants is crucial for determining their values based on given information.
Reference angles in all four quadrants help determine trigonometric function values by relating them to angles in the first quadrant.
Algebraic methods can be used to find trigonometric function values based on known information about a specific angle and quadrant.
Graphs of sine and cosine functions show oscillating curves with key values at every PI/2, with the cosine graph being a shifted version of the sine graph.
The periodic nature of sine and cosine functions with values constrained between plus/minus 1 and key values occurring regularly every PI/2.- Transformations can affect the shapes of curves, including parabolas, sine, and cosine functions, involving vertical and horizontal shifting, stretching, and flipping.
The period of a function determines its repetition within regular intervals, while the fundamental period helps track shifting and stretching of the function's period.
The midline of a function cuts it vertically in half and is primarily affected by vertical shifts.
The amplitude of a function measures the vibrations' range from the midline to the maximum or minimum points.
Graphing transformations involves identifying the fundamental period, determining key values, transforming corresponding y-coordinates, and plotting points.
Shifting transformations involve adding or subtracting values to the function or its argument for horizontal or vertical shifts.
Stretching transformations come from multiplying the entire function or argument by a value for horizontal or vertical stretches.
The general transformation formula is y = a*f(bx - c) + d, with a specific order of operations: horizontal shift, horizontal stretch, vertical stretch, and vertical shift.
Tangent functions have specific zeros and vertical asymptotes that help in graphing, following periodicity with a fundamental period of negative PI/2 to PI/2.
Graphing reciprocals involves understanding that large X values result in small reciprocals and small X values lead to large reciprocals, except for +/-1.