MAT 130 - Trigonometry

1. Interpret angles and their measure
   1. Draw angles whose measures are given in degrees and radians
   2. Convert degree-minutes-seconds to decimal degrees
   3. Determine a positive angle less than one revolution that is coterminal with a given angle
   4. Convert degree measure to radian measure and vice versa
   5. Determine arc length and the area of a sector
2. Establish the trigonometric functions on a unit circle
   1. Determine sine, cosine, and tangent using the unit circle
   2. Determine the reciprocal functions using the unit circle
   3. Make sense of the eight fundamental identities
   4. Use the fundamental identities to simplify trigonometric expressions
   5. Evaluate trigonometric functions using the fundamental identities
   6. Determine the values of trigonometric functions
   7. Identify the signs of the trigonometric functions by quadrant
3. Assess trigonometric functions
   1. Interpret the generalized definition of the trigonometric functions
   2. Evaluate the trigonometric functions given a point on the terminal side
   3. Find the reference angle for any given triangle
   4. Evaluate trigonometric functions of real numbers by table/calculator
   5. List the exact values for the trigonometric functions pi/6, pi/4, pi/3, pi/2, pi
   6. Analyze the trigonometric functions using a table/calculator
   7. Determine the domain and range
4. Graph trigonometric functions
   1. Sketch the standard forms of the cosine, sine, tangent, secant, cosecant, and cotangent curves from memory
   2. Graph by plotting points
   3. Analyze and sketch trig functions using amplitudes, periods, and phase shifts
5. Investigate trigonometric identities.
   1. Apply trigonometric identities to write equivalent forms of expressions
   2. Prove identities using a variety of techniques
   3. Prove or disprove that a given equation is an identity
   4. Find exact values by using identities
6. Solve trigonometric equations
   1. Solve linear trigonometric equations
   2. Solve quadratic trigonometric equations
   3. Solve trigonometric equations by using identities
   4. Determine solutions to trigonometric equations with multiple angles
7. Investigate inverse trigonometric functions
   1. Determine inverse trigonometric relations and functions
   2. Evaluate inverse functions
   3. Sketch the inverse function
   4. Determine the Domain and Range of Inverse Functions
8. Investigate the right triangle definition of the trigonometric function
   1. State the right-triangle definition of the trigonometric functions
   2. Solve right triangle problems
   3. Solve solutions to problems using the Law of Cosines
   4. Solve problems using the Law of Sines
   5. Find the area of any triangle.
   6. Find the area of a sector of a circle
9. Utilize complex numbers and polar form
   1. Plot complex numbers and polar coordinates
   2. Convert complex numbers into trigonometric form
   3. Convert complex numbers into rectangular form
   4. Convert between polar and rectangular form and vice versa.
   5. Use DeMoivre’s Formula to raise complex numbers to integral powers and to find the nth roots of a complex number
10. Analyze conic sections using rectangular coordinates
    1. Formulate the standard equation of a parabola, an ellipse, and a hyperbola
    2. Determine the vertex, focus, and directrix of a parabola
    3. Determine the center, vertices, foci, and eccentricity of an ellipse
    4. Determine the center, vertices, foci, and asymptotes of a hyperbola
    5. Classify a conic from its general equation
11.   Examine the graph of polar-form curves (cardioid, rose, limaçon, and lemniscate)