Trigonometry and Advanced Mathematics

Concepts / Competencies / Assessment / Standards
Trigonometric Functions / Convert decimal degrees to degrees, minutes and seconds and vice versa; define
and use coterminal and reference angles / Hwk / CC.2.3.HS.A.7
Find the values of the six trigonometric rations for acute angles of right triangles.
Use the mnemonic SOHCAHTOA / Hwk / CC.2.3.HS.A.7
CC.2.2.HS.C.9
Develop the unit circle from the 2 special right triangles, 30-60-90 and 45-45-90 / Hwk/Quiz / CC.2.3.HS.A.7
Use SOHCAHTOA to find the measures of the sides of right triangles. / Hwk / CC.2.3.HS.A.7
Use SOHCAHTOA to find the measures of the angles of right triangles
Solve real world applications of right triangles / Hwk/Quiz / CC.2.3.HS.A.14 CC.2.3.HS.A.7
Use the Law of Sines to find measures of sides and angles of triangles that are not right triangles
Find areas of non-right triangles / Hwk / CC.2.3.HS.A.3
Use the Ambiguous Case of the Law of Sines to determine if zero, one, or two triangles can be constructed from given information / Hwk / CC.2.3.HS.A.3
Use the Law of Cosines to find the measure of a side or angle of a non-right triangle when Law of Sines is not applicable / Hwk/Quiz / CC.2.3.HS.A.3
Unit test
Concepts / Competencies / Assessment / Standards
Graphs of the Trigonometric Functions / Change from radian measure to degree measure, and vise versa.
Find the arc length of a circle, and find area of a sector of a circle / Hwk / CC.2.3.HS.A.8
CC.2.2.HS.C.7
Find linear and angular velocity / Hwk/Quiz
Derive and draw the graphs of the Sine and Cosine Functions / Hwk / CC.2.2.HS.C.8
Define and find the amplitude and period to draw graphs of the Sine and Cosine Functions.
Write equations given amplitude and period for Sine and Cosine Functions / Hwk / CC.2.2.HS.C.4
CC.2.2.HS.C.8
Define and find the phase shift and vertical translation to draw graphs of the Sine and Cosine Functions / Hwk/Quiz / CC.2.2.HS.C.4
Model real world data using Sine and Cosine Functions / Hwk / CC.2..3HS.A.14
Graph the Remaining Trig Functions: Tangent, Secant, Cosecant, Cotangent, / Hwk / CC.2.2.HS.C.8
Graph the inverse Trig Functions / Hwk / CC.2.2.HS.C.4
Unit test
Concepts / Competencies / Assessment / Standards
Trigonometric Identities
and Equations / Identify and use Reciprocal Identities, Quotient Identities, and Pythagorean
Identities to simplify expressions. / Hwk /
CC.2.2.HS.C.9
Verify Trigonometric Identities / Hwk/Quiz
Use the Sum and Difference Identities for Sine, Cosine, and Tangent / Hwk/Quiz
Use the Double and Half-Angle Identities for Sine, Cosine, and Tangent / Hwk/Quiz
Solve Trigonometric Equations / Hwk/Quiz / CC.2.2.HS.C.9
Unit test
Concepts / Competencies / Assessment / Standards
Polar Coordinates and
Complex Numbers / Graph points in polar coordinates, graph polar equations, determine the distance
between 2 points with polar coordinates. / Hwk
Graph various polar equations; such as cardiod, limacon, rose, etc / Hwk/Quiz
Convert between polar and rectangular coordinates, and vice versa / Hwk
Write and graph the polar from of a linear equation / Hwk
Perform all the operations on complex numbers in rectangular form / Hwk/Quiz / CC.2.1.HS.F.6
Graph complex numbers in the complex number and convert them to polar from and vice versa / Hwk
Multiply and Divide Complex Numbers in Polar Form / Hwk
Find Powers and Roots of Complex Numbers in polar form using De Moivre’s Theorem / Hwk
Unit test
Concepts / Competencies / Assessment / Standards
Conic Sections / Find the distance and midpoint between 2 points on the coordinate plane / Hwk
Use and determine the standard form of a circle by determining the center and radius / Hwk/Quiz / CC.2.3.HS.A.10
Use and determine the standard form of an ellipse by determining the center, vertices, and foci / Hwk/Quiz / CC.2.3.HS.A.10
Use and determine the standard form of a hyperbola by determining the center, the vertices, the foci, and the asymptotes / Hwk/Quiz / CC.2.3.HS.A.10
Use and determine the standard form of a parabola by determining the vertex, the focus, the directrix, and axis of symmetry / Hwk/Quiz / CC.2.3.HS.A.10
Unit test
Concepts / Competencies / Assessment / Standards
Exponential and Logarithmic Functions / Use the properties of exponents, and simplify rational exponents / Hwk / CC.2.1.HS.F.1
Graph exponential functions. Solve problems using exponential growth and decay / Hwk / CC.2.2.HS.C.5
CC.2.2 HS.D.9
Use the natural base e to graph functions, solve problems using e. / Hwk/Quiz / CC.22.HS.D.10
Evaluate expressions using logarithms, solve logarithmic equations, graph
Logarithmic equations / Hwk / CC.2.2.HS.C.5
CC.2.2 HS.D.9
Use natural logs, ln, to solve equations, Graph natural log, ln, functions / Hwk / CC.2.2.HS.C.5
CC.2.2 HS.D.9
Solve real world problems using natural logarithmic functions / Hwk/Quiz / CC.2.2.HS.C.5
CC.2.2 HS.D.9
Unit test
Concepts / Competencies / Assessment / Standards
Sequences and Series / Define and use arithmetic sequence and series to find the nth term of a sequence
and find the sum of n terms of an arithmetic series / Hwk
Define and use geometric sequence and series to find the nth term of a sequence and find the sum of n terms of a geometric series / Hwk/Quiz
Find the limit of the terms of an infinite sequence. Find the sum of an infinite
Geometric series / Hwk
Define convergent and divergent series and determine whether a series is which of the two / Hwk/Quiz
Use sigma notation to find sums and be able to express a series in sigma notation / Hwk
Use the Binomial Theorem and Pascal’s Triangle to expand binomials / Hwk/Quiz
Unit test
Concepts / Competencies / Assessment / Standards
Combinatorics and Probability / Solve problems using the Basic Counting Principle, solve problems using
Permutations and Combination s / Hwk
Solve problems that involve permutations with repetitions and circular permutations / Hwk/Quiz
Find the probability of an event, find the odds for the success and failure of an
event. / Hwk / CC.2.4.HS.B.7
Find the probabilities of: independent and dependent events, and mutually
Inclusive and Exclusive events / Hwk/Quiz / CC.2.4.HS.B.7
Find the probability of an event given the occurrence of another event / Hwk / CC.2.4.HS.B.7
CC.2.4.HS.B.6
Find the probability of an event using the Binomial Theorem / Hwk/Quiz / CC.2.4.HS.B.7
Unit test
Concepts / Competencies / Assessment / Standards
Statistics and Data Analysis / Draw, analyze, and use bar graphs and histograms. Organize data into a frequency
Distribution. / Hwk / CC.2.4.HS.B.1
Find the mean, median, and mode of a set of data. Construct and analyze a stem and leaf plot / Hwk / CC.2.4.HS.B.1
CC.2.4.HS.B.2
Construct a box and whisker plot. Find interquartile range, mean and standard
Deviations. / Hwk/Quiz / CC.2.4.HS.B.1
CC.2.4.HS.B.2
Use the normal distribution curve / Hwk / CC.2.4.HS.B.1
CC.2.4.HS.B.4
Find the standard error of the mean to predict the true mean of a population with
a certain level of confidence / Hwk/Quiz / CC.2.4.HS.B.4
CC.2.4.HS.B.5
unit test
Concepts / Competencies / Assessment / Standards
Calculus / Calculate limits algebraically and by using a calculator
Find derivatives and antiderivatives of polynomials
Find areas of integrals of polynomial functions and find the areas under their
graphs.