Download MTH 181 Core Objectives - Mathematics

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.