Trigonometry

Unit 1

• F.IF.7.e – Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
• F.IF.8.b – Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)ᵗ, y = (0.97)ᵗ, y = (1.01)12ᵗ, y = (1.2)ᵗ/10, and classify them as representing exponential growth or decay.

Unit 2

• F.TF.1 – Understand radian measure of an angle as the length of the arc on the unit circle substended by the angle.
• F.TF.2 – Explain how the unit circle and the coordinate plane enables the extension of trigonometric functions to all real numbers. Interpret as radian measures transversed counter-clockwise around the unit circle.
• F.TF.3 – Use special triangles to determine geometrically the value of sin, cosine, tangent for π/3, π/4, π/6 and use the unit circle to express the value of sin, cosine and tangent for x, π + x and 2π – x, in terms of their values for x where x is any real number.
• F.TF.4 – Use the unit circle to explain the symmetry (odd and even) and periodicity of trigonometric functions.

Unit 3

• F.TF.5 – Choose trigonometric functions to model periodic phenomenon with specific amplitude, frequency and midline.
• F.TF.6 – Understand that restrictions of trigonometric functions to a domain which is always increasing or always decreasing allows its inverse to be constructed.
• F.TF.7 – Use inverse functions to solve trigonometric equations that arise in modeling to context; evaluate the solutions using technology, and interpret them in terms of context.

Unit 4

• F.TF.8 – Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
• F.TF.9 – Analyze trigonometric identities and use them to simplify trigonometric functions and solve trigonometric equations. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Unit 5

• G.SRT.9 – Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
• G.SRT.10 – Prove the Laws of Sines and Cosines and use them to solve problems.
• G.SRT.11 – Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

Unit 6

• N.VN.1 – 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||, v).
• N.VN.2 – Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
• N.VN.3 – Solve problems involving velocity and other quantities that can be represented by vectors.
• N.VN.4.a – 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.
• N.VN.4.b – Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
• N.VN.4.c – 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.
• N.VN.5.a – 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).

N.VN.5.b – 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).

This course is offered as dual credit through University of Missouri: St. Louis.^*

* Course offerings are dependent on enrollment and instructor availability.

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