| Originator: | Brown, Clark Status: Approved Department: MAT Mathematics |
| Date Created: | 03/10/2017 Submitted: 03/23/2017 Completed: 05/09/2017 |
| Effective Semester: | Fall |
| Catalog Year: | 2018-19 |
| Course Prefix: | MAT |
| Course Number: | 181 |
| Course Full Title: | Plane Trigonometry |
| Old course information: | |
| Reason for Evaluation: | Goals, Competencies and/or Objectives Change |
| Current Credit: | 3 |
| Lecture Hours: | 3 |
| Lab Hours: | 0 |
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| If the credit hour change box has been marked, please provide the new credit hour: | |
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| SUN Course?: | No |
| AGEC Course?: | Yes |
| Articulated?: | Yes |
| Transfer: | ASU NAU UA |
| Prerequisite(s): | Grade of "C" or better in MAT 151, or appropriate score on the college's math placement test |
| Corequisite(s): | None |
| Catalog Course Description: | A study of the trigonometric functions and their graphs and inverses, trigonometric identities, and the applications of these functions to right and oblique triangles, vectors, complex numbers, and polar and parametric equations. |
| Course Learning Outcomes: | 1. Express the trigonometric functions in terms of the terminal side of an angle, right triangles, and the unit circle. (2)
2. Simplify trigonometric expressions using both degree and radian measure, exact trigonometric function values for special angles, and trigonometric identities. (3,5) 3. Graph trigonometric functions and their transformations. (5,6) 4. Solve analytic and applied problems involving trigonometric equations, right and oblique triangles, vectors, complex numbers, and polar and parametric equations. (3,5,6) |
| Course Competencies: | Competency 1 Express the trigonometric functions in terms of a point in the Cartesian plane on the terminal side of an angle.
Objective 1.1 Convert between decimal degree and degree-minute-second (DMS) format for angle measure. Objective 1.2 Perform angle operations using decimal degree and DMS format. Objective 1.3 Solve applied problems using the basic relationships of similar triangles, vertical angles, and the angle sum of a triangle. Objective 1.4 Express the trigonometric functions as ratios of x, y, and r, where (x,y) is a point on the terminal position of an angle and r is the distance of (x,y) from the origin. Objective 1.5 Simplify trigonometric expressions using the reciprocal, Pythagorean, and quotient identities. Objective 1.6 Identify the sign of each trigonometric function in each quadrant of the Cartesian plane. Objective 1.7 Identify the exact trigonometric function values for quadrantal angles. Competency 2 Express the trigonometric functions in terms of right triangles. Objective 2.1 Define the trigonometric functions for acute angles of a right triangle. Objective 2.2 Define the trigonometric functions for non-acute angles using reference angles. Objective 2.3 Identify the exact trigonometric function values for 30, 45, and 60-degree reference angles in each quadrant. Objective 2.4 Simplify trigonometric expressions using the co-function identities. Objective 2.5 Compute trigonometric function values using a calculator. Objective 2.6 Solve right triangle problems, including angle of elevation/depression and bearing problems, using the trigonometric relationships. Competency 3 Express the trigonometric functions in terms of the unit circle. Objective 3.1 Define radian measure. Objective 3.2 Convert between radians and degrees. Objective 3.3 Identify the corresponding radian measure for quadrantal angles and 30, 45, and 60-degree reference angles in each quadrant. Objective 3.4 Identify the exact trigonometric function values for special angles given in radian measure. Objective 3.5 Compute the arc length of a portion of a circle using the radian measure of an angle. Objective 3.6 Compute the area of a sector of a circle using the radian measure of an angle. Objective 3.7 Extend the domain of the trigonometric functions from angles to the real numbers. Objective 3.8 Define the trigonometric functions in terms of arc lengths on the unit circle. Objective 3.9 Solve problems involving the relationship between linear and angular speed. Competency 4 Graph trigonometric functions. Objective 4.1 Identify the basic graphs of the six trigonometric functions. Objective 4.2 Identify the key features of a periodic function from its equation, including amplitude, period, phase shift and vertical translation. Objective 4.3 Graph trigonometric functions by using the key features and transformations of the basic graphs of the six trigonometric functions. Objective 4.4 Model the simple harmonic motion of periodic phenomena using trigonometric expressions. Competency 5 Verify trigonometric identities. Objective 5.1 Identify the reciprocal, quotient, co-function, Pythagorean, and negative angle identities. Objective 5.2 Identify the sum and difference identities for cosine, sine, and tangent. Objective 5.3 Identify the double- and half-angle identities for cosine, sine, and tangent. Objective 5.4 Identify the power-reducing, product-to-sum and sum-to-product identities for sine and cosine. Objective 5.5 Simplify trigonometric expressions using the above identities. Objective 5.6 Verify trigonometric identities using the above identities and algebraic and graphical techniques. Competency 6 Solve algebraic equations involving trigonometric functions using the inverse trigonometric functions. Objective 6.1 Identify appropriate domain restrictions to define the inverse trigonometric functions. Objective 6.2 Identify the basic graphs of the inverse trigonometric functions including their domain and range. Objective 6.3 Solve trigonometric equations using identities, factoring, and linear and quadratic methods. Objective 6.4 Solve trigonometric equations with half-angles and multiple angles. Objective 6.5 Solve equations involving inverse trigonometric functions. Competency 7 Solve oblique triangle and vector problems using trigonometry. Objective 7.1 Solve SAA and ASA triangles using the law of sines. Objective 7.2 Solve SSA triangles, including the ambiguous case, using the law of sines. Objective 7.3 Solve SAS and SSS triangles using the law of cosines. Objective 7.4 Compute the area of an oblique triangle. Objective 7.5 Perform vector operations both graphically and algebraically. Objective 7.6 Compute the angle between two vectors using the dot product. Objective 7.7 Solve angle of incline and navigation applications using vectors. Competency 8 Solve problems involving complex numbers and polar and parametric equations using trigonometry. Objective 8.1 Convert between the trigonometric (polar) form of a complex number and its rectangular form. Objective 8.2 Multiply complex numbers in polar form using the product theorem. Objective 8.3 Divide complex numbers in polar form using the quotient theorem. Objective 8.4 Find powers and roots of complex numbers using DeMoivre's Theorem. Objective 8.5 Contrast the polar coordinate system with the rectangular system. Objective 8.6 Graph polar equations. Objective 8.7 Convert between polar and rectangular equations. Objective 8.8 Describe a plane curve using parametric equations. Objective 8.9 Graph plane curves defined parametrically. Objective 8.10 Find the rectangular equivalent to a parametric graph. Objective 8.11 Solve applied problems modeled using parametric equations. |