
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: Prerequisite: 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 degreeminutesseconds 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 righttriangle 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 polarform curves (cardioid, rose, limaçon, and lemniscate)
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