Guiding Principles of Mathematics Instruction:

• Mathematical proficiency is defined by conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition (National Research Council, 2001).
• Mathematical proficiency drives independent thinking, reasoning, and problem-solving.
• Mathematical proficiency is the foundation for careers in science, technology, engineering and mathematics (STEM), and it is increasingly becoming the foundation for careers outside of STEM (NCTM, 2018)
• Effective mathematics teaching “engages students in meaningful learning through individual and collaborative experiences that promote their ability to make sense of mathematical ideas and reason mathematically” (NCTM, 2014).
• Standards-based instruction accelerates student gains.
• Students construct mathematical knowledge through exploration, discussion, and reflection.
• Teachers are facilitators of student learning, as they engage students in rich tasks. Administrators are change agents and have the power to create and to support a culture of mathematical proficiency.
TR.UC.2

High School

H.S. Precalculus: Trigonometry

Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

TR.UC.3

High School

H.S. Precalculus: Trigonometry

Use special triangles to determine the values of sine, cosine, and tangent for π/3, π/4, and π/6. Apply special right triangles to the unit circle and use them to express the values of sine, cosine, and tangent for x, π ± x, and 2π ± x in terms of their values for x, where x is any real number.

TR.V.1

High School

H.S. Precalculus: Trigonometry

Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||).

TR.V.2

High School

H.S. Precalculus: Trigonometry

Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

TR.V.3

High School

H.S. Precalculus: Trigonometry

Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

TR.V.4

High School

H.S. Precalculus: Trigonometry

Understand vector subtraction v - w as v + (-w), where -w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

TR.V.5

High School

H.S. Precalculus: Trigonometry

Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).

TR.V.6

High School

H.S. Precalculus: Trigonometry

Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).

TR.V.7

High School

H.S. Precalculus: Trigonometry

Solve problems involving velocity and other quantities that can be represented by vectors.