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Curriculum Guide

Elementary Analysis Page 11

Prove and apply
trigonometric
identities

HSF.TF.C.8

Prove the Pythagorean identity sin^2 (θ) + cos^2

Simplify trigonometric expressions/prove and solve

trigonometric equations

(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.

Use the Law of Sines and Law of Cosines to find

unknown parts of a triangle

Prove the double angle formulas for sine and cosine

and use them to solve problems.

Advanced

Mathematics

Text

8-1, 8-4, 8-5

Chapter 9

10-3

Graphing

Calculators

EXPRESSING
GEOMETRIC
PROPERTIES WITH
EQUATIONS

Translate between the
geometric description
and the equation for a
conic section

HSG.GPE.A.1

HSG.GPE.A.2

HSG.GPE.A.3

HSA.REI.C.7

Derive the equation of a circle of given center and

radius using the Pythagorean Theorem; complete the

square to find the center and radius of a circle given

by an equation.

Derive the equation of a parabola given a focus and

directrix.

(+) Derive the equations of ellipses and hyperbolas

given the foci, using the fact that the sum or

difference of distances from the foci is constant.

Solve a simple system consisting of a linear equation

and a quadratic equation in two variables algebraically

and graphically. For example, find the points of

intersection between the line y = -3x and the circle x^2 +

y^2

= 3.

Advanced

Mathematics

Text

6-1 to 6-5

Graphing

Calculators

10 days