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Student Name________________________________ Instructor Name_________________________________ High School or Vocational Center_________________________________________Grade________________ COMPETENCY RECORD FOR ARTICULATION Muskegon Community College Mathematics Please check below each skill the student has mastered as described, with 80 percent accuracy, or with an A or B grade. The skills needed for articulation of each course are listed. MTH 112 Trigonometric Functions with Coordinate Geometry 4 Credit Hours Task Satisfactory Trigonometric functions based on the unit circle; applications using other circles 1. Be able to find, on a unit circle, the terminal point for a given angle and the reference number for a given terminal point. 2. Be able to find the sine, cosine, tangent, cotangent, secant, and cosecant of a given angle using the unit circle. 3. Be able to find the values of the six basic trigonometric functions π π π π for these special angles (in radians): 0, , , , , and π . 6 4 3 2 4. Be able to identify which of the six basic trigonometric functions are even functions and which are odd functions. 5. Be able to use the fundamental trigonometric identities (reciprocal and Pythagorean identities) to simplify an expression. 6. Be able to convert angle measurement between degrees and radians. 7. Be able to determine the length of the arc of a circle, given an angle and radius. 8. Be able to determine the area of a circular sector, given an angle and radius. Trigonometric functions based on the right triangle; applications using other triangles 1. Be able to find trigonometric functions of a right triangle using adjacent sides, opposite sides, and/or the hypotenuse. MTH 112 - 6/9/08 Unsatisfactory Task Satisfactory Unsatisfactory 2. Be able to find the trigonometric ratios of the special right triangles (30-60-90 and 45-45-90). 3. Be able to solve a right triangle. 4. Be able to use the reference angle to evaluate a trigonometric function. 5. Be able to determine the area of a triangle. 6. Be able to use the Law of Sines to solve a triangle. 7. Be able to use the Law of Cosines to solve a triangle. 8. Be able to Heron’s Formula to find the area of a triangle. 1 s ( s − a )( s − b)( s − c) where s= (a+b+c) is the 2 semiperimeter (half the perimeter) of a triangle with sides a, b, and c. Area = Trigonometric graphs 1. Be able to graph the six basic trigonometric functions. 2. Be able to graph transformations of six basic trigonometric functions including: changes in amplitude, phase shift, and/or period. Analytic trigonometry, inverse trigonometric functions, complex number forms 1. Be able to prove and use the following identities and formulas to find trigonometric values and solve trigonometric equations: Cofunctions identities Addition and subtraction formulas; sums of sines and cosines Double-angle identities Half-angle identities (and related formulas for lowering powers) Product-sum identities 2. Be able to solve trigonometric equations by factoring. 3. Be able to graph the inverse trigonometric functions. 4. Be able to find the composition of trigonometric functions and their inverses. 5. Be able to evaluate the inverse trigonometric functions. 6. Be able to find the points of intersection for two trigonometric functions. 7. Be able to find the trigonometric form of complex numbers, including modulus and argument. MTH 112 2 Task Satisfactory Unsatisfactory 8. Be able to perform multiplication and division of complex numbers. 9. Be able to find the power of a complex number using DeMoivre’s Theorem: If z=r(cosθ + i sin θ), then for any integer n, zn = rn(cos nθ + i sin nθ ) 10. Be able to find the nth roots of a complex number: If z = r (cos θ + i sin θ), and n is a positive integer, then z has the n distinct nth roots: 1 θ + 2kn θ + 2kn r n cos + i sin for k = 0, 1, 2, ..., n - 1 n n Vectors 1. Be able to identify the initial and terminal points of a vector. 2. Be able to find the sum and difference of two vectors. 3. Be able to find perform scalar multiplication of a vector. 4. Be able to find the analytic form of a vector and i-j form of a vector. 5. Be able to find the magnitude (norm or length) of a vector. 6. Be able to apply the vector addition and scalar multiplication properties of vectors. 7. Be able to break down a vector into its horizontal and vertical components. MTH 112 3 Task Satisfactory Unsatisfactory Analytic geometry 1. Be able to graph and find the equation of a parabola with vertex at origin. 2. Be able to find the focus and directrix of a paraola. 3. Be able to graph and find the equation of an ellipse with center at origin. 4. Be able to find the foci of an ellipse. 5. Be able to find the eccentricity of an ellipse. 6. Be able to graph and find the equation of a hyperbola with center at origin. 7. Be able to find the vertices and asymptotes of a hyperbola. 8. Be able to find important values (foci, directrix, vertices, asymptotes) for conic functions subjected to horizontal and vertical shifts. 9. Be able to graph and find the general equation of a shifted conic section. 10. Be able to the XY-coordinates of a conic equation after the rotation of axes. 11. Be able to use the general conic equation Ax2 + Bxy + Cy2 + Dx + Ey + F =0 to eliminating the xy term in an equation. 12. Be able to use the general conic equation to identify a conic by its discriminant. Polar coordinates and equations 1. Be able to plot polar points. 2. Be able to convert between polar and rectangular coordinates. 3. Be able to graph polar equations. 4. Be able to recognize the common polar curves: circles, spirals, limaçons, roses, and lemniscates. 5. Be able to find the polar equation of a conic and use it to sketch the conic. Parametric equations 1. Be able to graph a parametric curve. 2. Be able to convert between parametric equations and rectangular functions. 3. Be able to convert bewteen polar equations and parametric forms. MTH 112 4 Task Satisfactory Unsatisfactory Sequences and series 1. Be able to find the terms in a non-recursive and recursive sequence. 2. Be able to identify the Fibonacci sequence. 3. Be able to compute the partial sum of a sequence. 4. Be able to use the sigma (Σ) notation of sums and apply the properties of sums. 5. Be able to find the terms and partial sums of an arithmetic sequence. 6. Be able to find the terms and partial sums of a geometric sequence. 7. Be able to find the next term in an infinite series. 8. Be able to find the sum of an infinite geometric series. Mathematical induction 1. Be able to distinguish betwen a conjecture and a mathematical proof. 2. Be able to demonstrate the principles of mathematical induction by doing a simple proof. Binomial theorem 1. Be able to generate expanded binomial coefficients using factorials: n n! = r r!(n − r )! 2. Be able to expand a binomial using Pascal’s triangle. 3. Be able to expand a binomial using the Binomial Theorem 4. Be able to find the general term of binomial expansion: n r n-r The term that contains ar in the expansion of (a+b)n is ab n − r Instructor’s Signature _____________________________________________________Date ______________ MTH 112 5