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Missouri State University Trigonometry - MTH 181 - Core Curriculum Objectives Using Larson’s Trigonometry, 9th edition CHAPTER 1: TRIGONOMETRY Section 1.1 - Radian and Degree Measure 1 Describe angles. 2 Use radian measure. 3 Use degree measure. 4 Use angles to model and solve real-life problems. Section 1.2 - Trigonometric Functions: The Unit Circle 1 Identify a unit circle and describe its relationship to real numbers. 2 Evaluate trigonometric functions using the unit circle. 3 Use domain and period to evaluate sine and cosine functions, and use a calculator to evaluate trigonometric functions. Section 1.3 - Right Triangle Trigonometry 1 Evaluate trigonometric functions of acute angles, and use a calculator to evaluate trigonometric functions. 2 Use the fundamental trigonometric identities. 3 Use trigonometric functions to model and solve real-life problems. Section 1.4 - Trigonometric Functions of Any Angle 1 Evaluate trigonometric functions of any angle. 2 Find reference angles. 3 Evaluate trigonometric functions of real numbers. Section 1.5 - Graphs of Sine and Cosine Functions 1 Sketch the graphs of basic sine and cosine functions. 2 Use amplitude and period to help sketch the graphs of sine and cosine functions. 3 Sketch translations of the graphs of sine and cosine functions. 4 Use sine and cosine functions to model real-life data. Section 1.6 - Graphs of Other Trigonometric Functions 1 Sketch the graphs of tangent functions. 2 Sketch the graphs of cotangent functions. 3 Sketch the graphs of secant and cosecant functions. Section 1.7 - Inverse Trigonometric Functions 1 Evaluate and know the properties of the inverse sine function. 2 Evaluate and know the properties of the other inverse trigonometric functions. 3 Evaluate the composition of trigonometric functions. Section 1.8 - Applications and Models 1 Solve real-life problems involving right triangles. 2 Solve real-life problems involving directional bearings. 3 Solve real-life problems involving simple harmonic motion. Missouri State University Trigonometry - MTH 181 - Core Curriculum Objectives Using Larson’s Trigonometry, 9th edition CHAPTER 2: ANALYTIC TRIGONOMETRY Section 2.1 - Using Fundamental Identities 1 Recognize and write the fundamental trigonometric identities. 2 Use the fundamental trigonometric identities to evaluate trigonometric functions, simplify trigonometric expressions, and rewrite trigonometric expressions. Section 2.2 - Verifying Trigonometric Identities 1 Verify trigonometric identities. Section 2.3 - Solving Trigonometric Equations 1 Use standard algebraic techniques to solve trigonometric equations. 2 Solve trigonometric equations of quadratic type. 3 Solve trigonometric equations involving multiple angles. 4 Use inverse trigonometric functions to solve trigonometric equations. Section 2.4 - Sum and Difference Formulas 1 Use the sum and difference formulas to evaluate trigonometric functions, verify identities, and solve trigonometric equations. Section 2.5 - Multiple-Angle and Product-to-Sum Formulas 1 Use the multiple-angle formulas to rewrite and evaluate trigonometric functions. 2 Use the power-reducing formulas to rewrite and evaluate trigonometric functions. 3 Use the half-angle formulas to rewrite and evaluate trigonometric functions. 4 Use product-to-sum and sum-to-product formulas to rewrite and evaluate trigonometric functions. 5 Use trigonometric formulas to rewrite real-life models. CHAPTER 3: ADDITIONAL TOPICS IN TRIGONOMETRY Section 3.1 - Law of Sines 1 Use the Law of Sines to solve oblique triangles (AAS or ASA). 2 Use the Law of Sines to solve oblique triangles (SSA). 3 Find the areas of oblique triangles. 4 Use the Law of Sines to model and solve real-life problems. Section 3.2 - Law of Cosines 1 Use the Law of Cosines to solve oblique triangles (SSS or SAS). 2 Use the Law of Cosines to model and solve real-life problems. 3 Use Heron's Area Formula to find the area of a triangle. Section 3.3 - Vectors in the Plane 1 Represent vectors as directed line segments. 2 Write the component forms of vectors. 3 Perform basic vectors operations and represent them graphically. 4 Write vectors as linear combinations of unit vectors. 5 Find the direction angles of vectors. Section 3.4 - Vectors and Dot Products 1 Find the dot product of two vectors and use the properties of the dot product. Missouri State University Trigonometry - MTH 181 - Core Curriculum Objectives Using Larson’s Trigonometry, 9th edition 2 Find the angle between two vectors and determine whether two vectors are orthogonal.