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Dec 14, 2024
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MAT 130 - Trigonometry Credits: 3 Lecture Hours: 3 Lab Hours: 0 Practicum Hours: 0 Work Experience: 0 Course Type: Core The central themes of this course include: circular functions and their inverses, trigonometric identities, trigonometric equations, solving triangles and graphing. Prerequisite: Pre-requisite: Minimum ALEKS scores of 46% or MAT 121 with a C- or better. Competencies
- Interpret angles and their measure
- Draw angles whose measures are given in degrees and radians
- Convert degree-minutes-seconds to decimal degrees
- Determine a positive angle less than one revolution that is coterminal with a given angle
- Convert degree measure to radian measure and vice versa
- Determine arc length and the area of a sector
- Establish the trigonometric functions on a unit circle
- Determine sine, cosine, and tangent using the unit circle
- Determine the reciprocal functions using the unit circle
- Make sense of the eight fundamental identities
- Use the fundamental identities to simplify trigonometric expressions
- Evaluate trigonometric functions using the fundamental identities
- Determine the values of trigonometric functions
- Identify the signs of the trigonometric functions by quadrant
- Assess trigonometric functions
- Interpret the generalized definition of the trigonometric functions
- Evaluate the trigonometric functions given a point on the terminal side
- Find the reference angle for any given triangle
- Evaluate trigonometric functions of real numbers by table/calculator
- List the exact values for the trigonometric functions pi/6, pi/4, pi/3, pi/2, pi
- Analyze the trigonometric functions using a table/calculator
- Determine the domain and range
- Graph trigonometric functions
- Sketch the standard forms of the cosine, sine, tangent, secant, cosecant, and cotangent curves from memory
- Graph by plotting points
- Analyze and sketch trig functions using amplitudes, periods, and phase shifts
- Investigate trigonometric identities.
- Apply trigonometric identities to write equivalent forms of expressions
- Prove identities using a variety of techniques
- Prove or disprove that a given equation is an identity
- Find exact values by using identities
- Solve trigonometric equations
- Solve linear trigonometric equations
- Solve quadratic trigonometric equations
- Solve trigonometric equations by using identities
- Determine solutions to trigonometric equations with multiple angles
- Investigate inverse trigonometric functions
- Determine inverse trigonometric relations and functions
- Evaluate inverse functions
- Sketch the inverse function
- Determine the Domain and Range of Inverse Functions
- Investigate the right triangle definition of the trigonometric function
- State the right-triangle definition of the trigonometric functions
- Solve right triangle problems
- Solve solutions to problems using the Law of Cosines
- Solve problems using the Law of Sines
- Find the area of any triangle.
- Find the area of a sector of a circle
- Utilize complex numbers and polar form
- Plot complex numbers and polar coordinates
- Convert complex numbers into trigonometric form
- Convert complex numbers into rectangular form
- Convert between polar and rectangular form and vice versa.
- Use DeMoivre’s Formula to raise complex numbers to integral powers and to find the nth roots of a complex number
- Analyze conic sections using rectangular coordinates
- Formulate the standard equation of a parabola, an ellipse, and a hyperbola
- Determine the vertex, focus, and directrix of a parabola
- Determine the center, vertices, foci, and eccentricity of an ellipse
- Determine the center, vertices, foci, and asymptotes of a hyperbola
- Classify a conic from its general equation
- Examine the graph of polar-form curves (cardioid, rose, limaçon, and lemniscate)
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