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# MAT 130 - Trigonometry

Credits: 3
Lecture Hours: 3
Lab Hours: 0
Practicum Hours: 0
Work Experience: 0
Course Type: Core

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
1. Use angle and degree measure
1. Draw angles whose measures are given in degrees
2. Convert degree-minutes-seconds to decimal degrees
3. Find a positive angle less than one revolution that is coterminal with a given angle
2. Use radian measure of angles
1. Draw angles whose measures are given in radians
2. Convert degree measure to radian measure
3. Convert radian measure to degree measure
4. Find arc length
3. Develop the trigonometric functions on a unit circle
1. Define sine, cosine, and tangent using the unit circle
2. Define the reciprocal functions including domain and range
3. State the eight fundamental identities
4. Use the fundamental identities to simplify trigonometric expressions
5. Use the fundamental identities to evaluate trigonometric functions
6. Find the values of trigonometric functions
7. Identify the signs of the trigonometric functions by quadrant
8. Examine the trigonometric functions using a table/calculator
4. Develop a generalized definition of the trigonometric functions
1. State 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 p/6, p/4, p/3, p/2, p,
5. Graph trigonometric curves 3p/2, and 2p radians
1. Sketch the standard forms of the cosine, sine, tangent, secant, cosecant, and cotangent curves from memory
2. Graph by plotting points
3. Sketch trig functions using various amplitudes, periods, and phase shifts
4. Graph the sum of two curves by adding ordinates
6. Investigate trigonometric identities.
1. Use 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
7. Apply trigonometric identities
1. Use the distance formula
2. Find the chord length given the central angle
3. Use the opposite-angle identities as an aid to graph certain trigonometric functions
4. Find exact values by using identities
8. Solve trigonometric equations
1. Solve linear trigonometric equations
2. Solve quadratic trigonometric equations
3. Solve trigonometric equations by using identities
4. Solve solutions to trigonometric equations with multiple angles
9. Investigate inverse trigonometric functions
1. Define inverse trigonometric relations and functions
2. Evaluate inverse functions
3. Draw a quick sketch of each inverse function
4. Use the reduction identity to simplify trigonometric equations
5. Use the reduction identity to graph trigonometric equations
10. 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
7. Solve applied problems using vector triangles
8. Write the algebraic representation of a vector
9. Determine the magnitude of a vector
10. Determine the scalar product of two vectors
11. Find the angle between two vectors
12. Determine whether two vectors are orthogonal
11. Use complex numbers
1. Add, subtract, multiply, and divide complex numbers
2. Find the absolute value of a complex number
3. Plot complex numbers in the Guassian plane
4. Write complex numbers in trigonometric form
5. Write complex numbers in rectangular form
6. Multiply and divide complex numbers in trigonometric form
7. Use DeMoivre’s Formula to raise complex numbers to integral powers and to find the nth roots of a complex number
12. Graph polar-form equations
1. Graph polar-form curves (cardiod, rose, and lemniscate) by plotting points
2. Find the intersection of polar-form curves

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