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