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Guiding Principles of Mathematics Instruction:
Standard | Grade | Area/Subject | Description |
---|---|---|---|
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. |