La Habra High School
Mathematics Department

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Trigonometry ICM Standards

TRIGONOMETRIC FUNCTIONS & APPLICATIONS

• identify parts of an angle.
• measure angles in radians, and degrees.
• convert from degrees to radians, and vice versa.
• use a scientific calculator to convert between degrees and radians.
• generate an angle on the unit circle.
• define sine and cosine functions.
• use the special angles in locating the coordinates of points on the unit circle.
• identify the graphs of the two functions.
• graph sine and cosine functions.
• generate coordinates of points derived from the special angles on the unit circle.
• define the six trig functions in terms of the x-coordinate, y-coordinate, and radius.
• derive the basic Pythagorean identity.
• complete appropriate proofs for other Pythagorean identities.
• apply sum and difference identities.
• evaluate and simplify expressions using appropriate identities.
• apply double angle, power reducing, and half angle identities.
• evaluate and simplify expressions using appropriate identities.
• graph sine and cosine functions with transformations.
• given graph and/or equation, identify amplitude, frequency, period, phase shift, and vertical shift.
• define and graph tangent and cotangent functions.
• identify tangent as slope.
• identify angle of inclination of a line.
• define the inverse trig functions.
• graph the inverse trig functions.
• solve a trig equation.
• compute the trig values at various standard angles.
• compute the inverse trig values at various standard points.
• use trig functions to solve right triangles.
• solve any triangle using Laws of Sines and Cosines.
• calculate the area of a triangle using appropriate formulas.
• convert between rectangle coordinates and polar coordinates.
• express rectangular equations in polar form and vice versa.
• graph polar equations.
• convert rectangular form to trigonometric/polar form and vice versa.
• graph a complex number.
• add, subtract, multiply, divide, and raise to a power complex numbers in rectangular form.
• multiply and divide complex numbers in trig/polar form.
• raise to powers and find the nth roots of complex numbers in trig/polar form.
• apply trigonometric functions to solve practical problem.

LINEAR ALGEBRA

• reduce a rectangular matrix to row echelon form.
• perform matrix addition and multiplication.
• invert a square matrix.
• use matrices to solve a system of linear equations.

MATHEMATICAL ANALYSIS

• define a vector.
• sketch a vector.
• write a vector in component form.
• perform vector addition and subtraction.
• perform multiplication (i.e., scalar multiple, scalar multiplication, and vector multiplication).
• solve work and force problems.
• identify and graph standard conic sections.
• rewrite the quadratic equation in standard form to identify the conic section.
• determine all pertinent points of the conic section.
• use translation and rotation formulas to graph a conic section.
• write an equation using a geometric description.
• determine the function.
• graph the function, sketching its asymptotes, if needed.
• change a function between parametric and rectangular form.
• graph a parametric function.

FUNCTIONS

• determine if a relation is a function, and justify the conclusion.
• determine domain and range from a graph, a set, or an equation.
• perform and evaluate composition of functions.
• find the inverse of a function.
• describe the effect of a rotation, translation and/or reflection on a function in the plane.

EXPONENTIAL & LOGARITHMIC FUNCTIONS

• demonstrate the laws of exponents in simplifying expressions.
• graph exponential functions.
• describe a relationship between exponents and logarithms.
• convert an exponential equation to a logarithmic equation and vice versa.
• solve problems using exponential and logarithmic concepts.
• manipulate logarithmic expressions.

SEQUENCES, SERIES, & LIMITS

• find the sum of a series.
• state the induction hypothesis.
• use induction to prove general statements.
• determine the limit of a sequence and a function.
• determine if simple sequences converge or diverge.