Trigonometric Functions and Graphs for General Studies
This free online course describes the graphs for trigonometric functions, as well as how to plot polar coordinates.Publisher: ADU
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Trigonometric Functions and Graphs for General Studies is the second in a series of trigonometry for general studies related courses. Why is trigonometry important? Trigonometry is one of the most important mathematical relationships. Triangles do not seem complex, but the application of triangles in mathematics has vital importance, especially where precise distance measurements are needed. Trigonometry can be a bit confusing, however, this course has been broken down into concise procedures to make your learning journey easy, detailed and interesting. This free online course begins by introducing you to various trigonometric identities which are used to solve many problems. Trigonometric Identities are useful whenever trigonometric functions are involved in an expression or an equation. There are various distinct identities involving the length as well as the angle of a triangle. A trigonometric identity is true for every possible value of the input variable on which it is defined. This course outlines the formulas for the basic identities and proceeds to show you how to prove for identities.
In this course, you will learn how to find the sine, cosine, and tangent of the sum or difference of two angles. Sine and cosine functions can be used to model many real-life situations, including electric currents, musical tones, radio waves, tides, and weather patterns. This course establishes that a distributive property does not apply to any of the six trigonometric functions. However, there are interesting relationships between the sum of two trigonometric functions and their product (or the product of two trigonometric functions and their sum). This course outlines the formula to convert the sum to product and product to sum. You will learn how to solve first- and second-degree trigonometric equations. You will also learn how to solve equations with more than one trig function. This course analyzes Inverse trigonometric functions. Inverses are used frequently in engineering, navigation, architecture, aeronautics and physics. Trigonometric functions and inverses can be used to find the side and measures of an angle.
Furthermore, this course discusses the graphs for the six trigonometric functions. For each graph, this course considers period, amplitude, frequency, domain and range. It illustrates in detail the application of the laws of sine and cosine. If you want to learn how to solve for the missing lengths and angle measures of a triangle, this course comes highly recommended. In rectangular coordinates: to locate a point, we move so many units left or right, and so many units up or down. When working in polar coordinates, we would often stop to think how far do we have to move from the pole, and in which direction? This course will help you learn how to plot points accurately on a polar coordinate system. This course further illustrates how to convert from rectangular to polar coordinates and vice versa. It is important to complete this course for a comprehensive understanding of the rules, theories and applications of trigonometry in general studies. So, register for this course and start your learning today.
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Trigonometric Identities and Equations
Trigonometric Identities and Equations - Learning Outcomes
Identities and Equations
Sine of the Sum or Difference of Two Angles
Double Angle Identities
Solving Trigonometric Equations
Trigonometric Identities and Equations - Lesson Summary
Trigonometric Identities and Equations - Assessment
Graphs of Trigonometric Functions
Graph of Trigonometric Function - Learning Outcomes
Sine and Cosecant Graphs
Inverse Trigonometric Functions
Applications of Laws Sine and Cosine
Graphs of Trigonometric Functions - Lesson Summary
Graphs of Trigonometric Functions - Assessment
Upon the successful completion of this course, you should be able to:
- Analyze how to plot points on the polar graph.
- Describe the Inverse sine function, Inverse cosine function and Inverse tangent function.
- Discuss the application of trigonometry in physics.
- State the law of cosines and sines.
- Summarize how to change from polar to rectangular coordinates and change from rectangular to polar coordinates.
- Distinguish between first-degree trigonometric equations and second-degree trigonometric equations.
- Define trigonometric identity and solve to prove identities.
- Identify the formulas for converting between degrees and radians.
- Distinguish the basic trigonometric Identities.
- Describe the double angle Identities for cosine, sine and tangents.
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