Dinwiddie County Subject: Trigonometry Scope and Sequence

Transcription

1 Dinwiddie County Subject: Trigonometry Scope and Sequence GRADE: High School 9 WKS Topics Equations (linear, quadratic, and absolute value) and Radicals (simplest radical form, including rationalizing the denominator using the conjugate) Angles In the Coordinate Plane (Standard Form) Targeted SOLS A.3, AII.3 T., T.3 Days Taught 6 Days 6 Days Essential Skills Resources Simplify radical expressions containing positive rational numbers and variables. Add and subtract radical expressions with like radicands. Multiply and divide radical expressions not requiring rationalizing the denominators. edhelper.com (Radicals - Advanced) Recognize and draw an angle in standard position. Use a conversion factor to convert from radians to degrees and vice versa without using a calculator. Textbook Section 5. (pgs ), Advanced Mathematics 7- (pgs. 57-6)

2 Arc Length and Sector Area G.0 8 Days The Six Trigonometric Ratios T., T. 5 Days The Unit Circle, Special Angles, and Reference Angles T.3, T.4 7 Days Calculate the area of a sector of a circle. Given the measure of a central angle and the radius of the circle, find the related arc length. Solve practical problems associated with circles, using properties of angles and arcs. Define the six circular trigonometric functions of an angle in standard position. Make the connection between the triangular and circular trigonometric Given one trigonometric function value, find the other five trigonometric function values. Find trigonometric function values of special angles and their related angles in both degrees and radians. Apply the properties of the unit circle without using a calculator. Use a conversion factor to convert from radians to degrees and vice versa without using a calculator. Use a calculator to find values of any angle in either degrees or radians. Textbook Section 5. (pgs ), Advanced Mathematics Section 7- (pgs ) Textbook Section 5.3 (pgs ), Advanced Mathematics Section 7-3 (pgs ) Textbook Section 5.3 (pgs , 44), Advanced Mathematics Section 7-4 (p , p )

3 Graphs of Trigonometric Functions T.4, T.6 0 Days Use a calculator to find values of any angle in either degrees or radians. Determine the amplitude, period, phase shift, and vertical shift of a trigonometric function from the equation of the function and from the graph of the function. Describe the effect of changing A, B, C, or D in the standard form of a trigonometric equation{e.g.,y = A sin (Bx + C) + D or y = A cos [B(x + C)] + D}. State the domain and the range of a function written in standard form {e.g., y = A sin (Bx + C) + D or y = A cos [B(x + C)] + D}. Sketch the graph of a function written in standard form {e.g., y = A sin (Bx + C) + D or y = A cos [B(x + C)] + D} by using transformations for at least one period or one cycle. Textbook Section 5.4, 5.5 (p , p ), Advanced Mathematics Section 7-4, 7-5, 8-, 8-3 (pgs , pgs )

4 Inverse Trigonometric Functions and their Graphs with Application to Angle of Inclination T.4, T.7 5 Days Define inverse trigonometric Find angle measures by using the inverse trigonometric functions when values are given. Find the domain and range of the inverse trigonometric Use the restrictions on the domains of the inverse trigonometric functions in finding the values of the inverse trigonometric Identify the graphs of the inverse trigonometric Textbook Section 5.6 (pgs ), Advanced Mathematics Section 7-6, 8- (pgs , pgs ) Trigonometric Equations T.8 5 Days Solve trigonometric equations with restricted domains algebraically and by using a graphing utility. Solve trigonometric equations with infinite it Textbook ksection ( (pgs solutions algebraically and 507), Advanced Mathematics by using a graphing utility. Section 8-, 8-5 (pgs , Check for reasonableness pgs ) of results, and verify algebraic solutions, using a graphing utility.

5 Algebraic Rational Expressions AII. 5 Days Add, subtract, multiply, and divide rational expressions whose denominators are monomials or polynomial expressions in completely factored form. Simplify a rational expression with common monomial or binomial factors. Recognize a complex fraction, and simplify it as a quotient or product of simple fractions. edhelper.com (Simplifying Algebraic Fractions) Trigonometric Expressions and Identities T.5 0 Days Use trigonometric identities to make algebraic substitutions to simplify and verify trigonometric identities. The basic trigonometric identities include- reciprocal identities; -Pythagorean identities; -Sum and difference identities; -Double-angle identities; & -Half-angle identities. Textbook Section 6., 6. (pgs ), Advanced Mathematics Section 8-4 (pgs. 37-3) Solving Right and Oblique Triangles with Application to Area T.9 5 Days Write a practical problem involving triangles. Solve practical problems involving triangles. Use the trigonometric functions, Pythagorean Theorem, Law of Sines, and Law of Cosines to solve practical problems. Identify a solution technique that could be used with a given problem. Textbook Section 5., 7., 7. (pgs , pgs ), Advanced Mathematics Section 9-, 9-, 9-3, 9-4 (pgs )