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Topic: Trigonometry 

Mathematics

 Standard 5.  Understands and applies basic and advanced properties of the concepts of geometry
  Level IV (Grade 9-12)
   Benchmark 7.Understands the basic concepts of right triangle trigonometry (e.g., basic trigonometric ratios such as sine, cosine, and tangent)
    Knowledge/skill statements
     1.Understands the concept of right triangle trigonometry
   Benchmark 8.Uses trigonometric ratio methods to solve mathematical and real-world problems (e.g., determination of the angle of depression between two markers on a contour map with different elevations)
    Knowledge/skill statements
     1.Understands the concept of tangent ratio
     2.Understands the concept of cosine ratio
     3.Understands the concept of sine ratio
     4.Determines whether a problem can be solved by using tangent ratios
     5.Determines whether a problem can be solved by using cosine ratios
     6.Determines whether a problem can be solved by using sine ratios
     7.Uses trigonometric ratios to solve problems of angle of depression on a contour map
     8.Understands the concept of angle of depression
 Standard 8.  Understands and applies basic and advanced properties of functions and algebra
  Level IV (Grade 9-12)
   Benchmark 3.Understands characteristics and uses of basic trigonometric functions (e.g., the sine and cosine functions as models of periodic real-world phenomena)
    Knowledge/skill statements
     1.Understands the concept of a cosine function
     2.Understands the concept of a sine function
     3.Understands the concept of a tangent function
     4.Understands that a sine function can model periodic phenomena
     5.Understands that a cosine function can model periodic phenomena
  Level V (Grade (College Readiness))
   Benchmark 7.Understands periodicity in the trigonometric functions and their graphs
    Knowledge/skill statements
     1.Understands the periodic nature of trigonometric functions
     2.Understands the periodic nature of trigonometric graphs
   Benchmark 8.Understands unit circle trigonometry
    Knowledge/skill statements
     1.Understands the concept of the unit circle
     2.Understands how trigonometric functions are defined on the unit circle
   Benchmark 9.Understands the Law of Sines, Law of Cosines, and basic trigonometric identities (e.g., double angle formulas, sum and difference identities)
    Knowledge/skill statements
     1.Understands the Law of Sines
     2.Understands the Law of Cosines
     3.Understands the double angle formulas
     4. Understands the trigonometric sum identities
     5. Understands the trigonometric difference identities
   Benchmark 10.Understands the graph of a function of the form f(t)=Asin(Bt+C)+D or g(t)=Acos(Bt+C)+D, in terms of amplitude, frequency, period, and vertical shift, and phase shift
    Knowledge/skill statements
     1.Understands the graph of the function of the form f(t) = A sin(Bt + C) + D in terms of amplitude
     2.Understands the graph of the function of the form f(t) = A sin(Bt + C) + D in terms of frequency
     3.Understands the graph of the function of the form f(t) = A sin(Bt + C) + D in terms of period
     4.Understands the graph of the function of the form f(t) = A sin(Bt + C) + D in terms of vertical shift
     5.Understands the graph of the function of the form f(t) = A sin(Bt + C) + D in terms of phase shift
     6.Understands the graph of the function of the form f(t) = A cos(Bt + C) + D in terms of amplitude
     7.Understands the graph of the function of the form f(t) = A cos(Bt + C) + D in terms of frequency
     8.Understands the graph of the function of the form f(t) = A cos(Bt + C) + D in terms of period
     9.Understands the graph of the function of the form f(t) = A cos(Bt + C) + D in terms of vertical shift
     10.Understands the graph of the function of the form f(t) = A cos(Bt + C) + D in terms of phase shift