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Greater Nanticoke Area School District
Trigonometry
Trigonometry includes the study of mathematics standards including
functions of acute angles, graphs of trigonometric functions, right triangles, oblique
triangles, fundamental identities and trigonometric equations.
Standard 2.3.11: Measurement and Estimation
CS 2.2.11B. Compare angles in degrees and radians
28. Convert from degrees to radians
29. Convert from radians to degrees
Standard 2.5 Mathematical problem Solving and Communication
CS 2.5.11A: Solve non-routine and multi-step problems
57. Apply basic rules of real numbers in problem solving
58. Select and justify appropriate methods needed in solving multi-step problems
CS 2.5.11B: Use representations to communicate mathematically
59. Translate words to symbols and symbols to words
60. Use appropriate mathematical terminology
61. Use appropriate mathematical rules
62. Interpret and explain data from a table or graph
Standard 2.8 Algebra and Functions
CS2.8.11A: Analyze and represent data
99. Represent a pattern graphically/ c. determine slope
Standard 2.9 Geometry
CS 2.9.11I: Model situations geometrically to formulate and solve problems
213. Use the special relationship that exists between pairs of angles formed by parallel
lines cut by transversal to solve problems and write proofs.
214. Use the measures of interior and exterior angles of a convex polygon to solve
problems.
215. Use the properties of congruent and similar polygons to solve problems and write
proofs.
217. Use the definition and properties of polygons to solve problems and write proofs.
Standard 2.10.11: Trigonometry (Right triangles; measuring and computing with triangles;
using graphing calculators )
CS 2.10.11A. Identify, create and solve practical problems involving triangles.
224. Use the Pythagorean Theorem to solve problems involving right triangles.
225. Define the six trigonometric functions:
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A. Sine
B. Cosine
C. Tangent
D. Cotangent
E. Secant
F. Cosecant
226. Use the six trigonometric functions to solve problems involving right triangles.
A. Solve problems involving labeled triangles
B. Angle of elevation
C. Angle of depression
D. Travel using compass directions
227. Use the laws of sines and cosines to solve problems involving triangles.
A. Solve problems involving non-right triangles
B. Classify given parts of triangles using SSS, SAS, ASA and SSA
C. Examine and solve problems of the "ambiguous case"
D. Use area formulas to solve problems
• K=1/2bh
• K=1/2 abSinC
• K=1/2a2 sinB SinC
Sin A
• K= s(s-a) (s-b) (sic) where s = a+b+c
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CS 2.10.11B. Graph and describe properties of periodic and circular functions.
228. Sketch a graph of each of the six trigonometric functions and identify the period
and/or amplitude.
229. Recognize and graph transformations or reflections of each of the six trigonometric
functions
A. y = A sin Bx and y = A cos Bx
B. y = A sin (Bx + C) and y= A cos (Bx + C)
230. Graph the inverse of each trigonometric function.
231. Determine the value the six trigonometric functions of an angle in standard position.
A. Define and use reference angles
B. Use positive and negative angles
C. Define and use co-terminal angles
232. Identify the relationship between angles in degree mode and radian mode.
233. Define the six trigonometric functions in terms of coordinates of points that satisfy
the equation x ^2+ y^2=1 (The Unit Circle)
234. Use graphing calculators to graph trigonometric functions.
CS 2.10.11C. Develop and use fundamental relationships among the trigonometric
functions.
235. Define the fundamental trigonometric identities.
A. Reciprocal
B. Quotient
C. Pythagorean
D. Sum and difference
E. Double angle
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236. Prove (verify) trigonometric identities.
A. Substitution
B. Factoring
C. Simplify trigonometric expressions
237. Solve equations involving trigonometric functions.
A. First Degree
B. Quadratic
C. Fractional
238. Solve trigonometric equations requiring the use of definitions, formulas, and
identities.
239. Solve trigonometric equations using tools of technology
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