A-C Valley Junior-Senior High School

Transcription

1 Course of Study A-C Valley Junior-Senior High School Page 1 of 12 Applied Trigonometry (NAME OF COURSE) GRADE LEVEL(S): 11 Educational Curriculum Level Person(s) Revising Curriculum (List Names) 1. Junior-Senior High School 1. Luke LaVan

2 Page 2 of 12 Subject/Discipline: Applied Trigonometry PA Academic Standards Category: 2.1 Major Concept: Numbers, Number Systems and Number Relationships Grade Level(s): 11 Solving linear, quadratic, and radical equations Add, subtract, multiply, and divide complex numbers A Use operations (e.g., opposite, reciprocal, absolute value, raising to a power, finding roots, finding logarithms)

3 Page 3 of 12 Subject/Discipline: Applied Trigonometry PA Academic Standards Category: 2.2 Major Concept: Computation and Estimation Grade Level(s): 11 Instructional Methods PA Academic Standards Assessment Materials / Resources Convert between radians and degrees Find the exact and approximate values of the six trig functions for an angle Find the exact and approximate angle that leads to a specific trig function value Apply right-triangle based trig to problems in surveying, navigation, construction, and angles of elevation/depression Provide algebraic and graphic calculator support to verify identities F Demonstrate skills for using computer spreadsheets and scientific and graphing calculators A Develop and use computation concept operations and procedures with real numbers in problemsolving situations E Recognize that the degree of precision needed in calculating a number depends on how the results will be used and the instruments used to generate the measure Add, subtract, multiply, and divide complex numbers Simplify powers of i Evaluate, solve, and graph exponential and logarithmic equations and apply to problem solving

4 Page 4 of 12 Subject/Discipline: Applied Trigonometry PA Academic Standards Category: 2.3 Major Concept: Measurement and Estimation Grade Level(s): 11 Calculate with degrees, minutes, seconds Convert between radians and degrees Find exact and approximate values of the six trig functions for an angle in radian measure Find the exact or approximate angle (in radians) that leads to a specific trig function value B Measure and compare angles in degrees and radians

5 Page 5 of 12 Subject/Discipline: Applied Trigonometry PA Academic Standards Category: 2.4 Major Concept: Mathematical Reasoning and Connections Grade Level(s): 11 Simplify trig expressions by writing in terms of sine and cosine Express one trig function in terms of another Prove identities by working with one side or by working with both sides Reciprocal Quotient Pythagorean Negative-angle Sum and difference Double angle Half angle A Use direct proofs, indirect proofs or proof by contradiction to validate conjectures C Determine the validity of an argument Provide algebraic and graphic calculator support to verify identities

6 Page 6 of 12 A-C VALLEY JUNIOR-SENIOR HIGH SCHOOL Subject/Discipline: Applied Trigonometry PA Academic Standards Category: 2.5 Major Concept: Mathematical Problem Solving and Communication Grade Level(s): 11 Classify angles Complementary and supplementary angles Vertical angles Angles formed by parallel lines cut by a transversal Classify triangles according to side and angles Use the Pythagorean Theorem to find a leg or a hypotenuse of a right triangle and solve related problems Write a trig function in terms of its co-function Solve equations using cofunction identities A Select and use appropriate mathematical concepts and techniques from different areas of mathematics and apply them to solving non-routine and multi-step problems B Use symbols, mathematical terminology, standard notation, mathematical rules, graphing and other types of mathematical representations to communicate observations, predictions, concepts, procedures, generalizations, ideas and results C Present mathematical procedures and results clearly, systematically, succinctly and correctly Apply right-triangle based trig to problems in surveying, navigation, construction, and angles of elevation/depression Apply trig function graphs to model situations D Conclude a solution process with a summary of results and evaluate the degree to which the results obtained represent an acceptable response to the initial problem and why the reasoning is valid

7 Page 7 of 12 A-C VALLEY JUNIOR-SENIOR HIGH SCHOOL Subject/Discipline: Applied Trigonometry PA Academic Standards Category: 2.5 Major Concept: Mathematical Problem Solving and Communication (Cont.) Grade Level(s): 11 Solve oblique triangles using the law of sines, law of cosines, of the ambiguous law of sines and apply to problem solving Evaluate, solve, and graph exponential and logarithmic equations and apply to problem solving A Select and use appropriate mathematical concepts and techniques from different areas of mathematics and apply them to solving non-routine and multi-step problems B Use symbols, mathematical terminology, standard notation, mathematical rules, graphing and other types of mathematical representations to communicate observations, predictions, concepts, procedures, generalizations, ideas and results C Present mathematical procedures and results clearly, systematically, succinctly and correctly D Conclude a solution process with a summary of results and evaluate the degree to which the results obtained represent an acceptable response to the initial problem and why the reasoning is valid

8 Page 8 of 12 Subject/Discipline: Applied Trigonometry PA Academic Standards Category: 2.8 Major Concept: Algebra and Functions Grade Level(s): 11 Solving linear, quadratic, and radical equations Graphing linear, quadratic, and radical equations Determining the domain and range of functions Solve equations using cofunction identities Solve quadratic equations for complex solutions Evaluate, solve, and graph exponential and logarithmic equations and apply to problem solving A Analyze a given set of data for the existence of a pattern and represent the pattern algebraically and graphically N Solve linear, quadratic and exponential equations both symbolically and graphically K Select, justify and apply an appropriate technique to graph a linear function in two variables, including slope-intercept, x- and y-intercepts, graphing by transformations and the use of a graphing calculator O Determine the domain and range of a relation, given a graph or set of ordered pairs D Formulate expressions, equations, inequalities, systems of equations, systems of inequalities and matrices to model routine and nonroutine problem situations

9 Page 9 of 12 Subject/Discipline: Applied Trigonometry PA Academic Standards Category: 2.9 Major Concept: Geometry Grade Level(s): 11 Use the Pythagorean Theorem to find a leg or a hypotenuse of a right triangle and solve related problems Find the distance between two points Find all angles that are co terminal to a given angle Find the exact and approximate values of the six trig functions for an angle I Model situations geometrically to formulate and solve problems G Solve problems using analytic geometry Find the exact and approximate angle that leads to a specific trig function value Find angle measure given an arc length and a radius Find the area of a sector of a circle Find linear and angular velocities and apply it to problem solving

10 Page 10 of 12 Subject/Discipline: Applied Trigonometry PA Academic Standards Category: 2.10 Major Concept: Trigonometry Grade Level(s): 11 Use the Pythagorean Theorem to find a leg or a hypotenuse of a right triangle and solve related problems Find the exact and approximate values of the six trig functions for an angle Find the exact and approximate angle that leads to a specific trig function value A Use graphing calculators to display periodic and circular functions; describe properties of the graphs B Identify, create and solve practical problems involving right triangles using the trigonometric functions and the Pythagorean Theorem Determine trig function values of an acute angle in a right triangle Find the measure of reference angles Solve right triangles Apply right-triangle based trig to problems in surveying, navigation, construction, and angles of elevation/depression Find exact and approximate values of the six trig functions for an angle in radian measure

11 Page 11 of 12 Subject/Discipline: Applied Trigonometry PA Academic Standards Category: 2.10 Major Concept: Trigonometry (Cont.) Grade Level(s): 11 Find the exact or approximate angle (in radians) that leads to a specific trig function value Graph sine, cosine, secant, cosecant, tangent, and cotangent equations with and without a calculator Determine the amplitude, period, phase shift, and vertical shift for the six trig functions and graph accordingly A Use graphing calculators to display periodic and circular functions; describe properties of the graphs B Identify, create and solve practical problems involving right triangles using the trigonometric functions and the Pythagorean Theorem and the Pythagorean Theorem Apply trig function graphs to model situations Find the area of an oblique triangle using Heron s formula

12 Page 12 of 12 Subject/Discipline: Applied Trigonometry PA Academic Standards Category: 2.11 Major Concept: Concepts of Calculus Grade Level(s): 11 Graph sine, cosine, secant, cosecant, tangent, and cotangent equations with and without a calculator Evaluate, solve, and graph exponential and logarithmic equations and apply to problem solving A Determine maximum and minimum values of a function over a specified interval B Interpret maximum and minimum values in problem situations C Graph and intercept rates of growth/decay