Unit+5

=Unit 5 Analytic Trigonometry=

=Project Grapher= [] =Video/Resources= []



**Objectives**
You will be able to justify the fundamental identities and use them to simplify trigonometric expressions. You will be able to use them to solve certain trigonometric equations.
 * Key Ideas**
 * Cofunction identities || Odd-even identities ||
 * Domain of validity || Pythagorean identities ||
 * Identity || Trigonometric equation ||
 * Video: Use the Fundamental Trigonometric Identities – Part A
 * Video: Use the Fundamental Trigonometric Identities – Part B

**Objectives**
You will be able to decide whether an equation is an identity and will be able to prove identities analytically.
 * Key Ideas**

Proof of an identity Word ladder
 * Video: Plan a Strategy for Verifying Trigonometric Identities
 * Video: Verify Trigonometric Identities
 * Video: Use Standard Algebraic Techniques to Solve Trigonometric Equations
 * Video: Solve Trigonometric Equations of Quadratic Type
 * Video: Solve Trigonometric Equations Involving Multiple Angles
 * Simulation: Solving Trigonometric Equations

**Objectives**
You will understand the derivations of, and be able to apply, the formulas for the cosine, sine, and tangent of a difference or sum.
 * Key Ideas**

Angle sum formula Reduction formula
 * Video: Use Sum and Difference Formulas

**Objectives**
You will understand the derivations of, and be able to apply, the double-angle, half-angle, and power reducing identities.
 * Key Ideas**

Double-angle identities Half-angle identities Power-reducing identities
 * Video: Use Multiple-Angle formulas to Rewrite and Evaluate Trigonometric Functions
 * Video: Use Half-Angle formulas to Rewrite and Evaluate Trigonometric Functions
 * Video: Use Product-to-Sum and Sum-to-Product Formulas

**Objectives**
You will be able to understand the proof of the Law of Sines and will be able to use the formula to solve a variety of problems.
 * Key Ideas**

Law of Sines Solving Triangles
 * Video: Use the Law of Sines to Solve Oblique Triangles (AAS or ASA)
 * Video: Use the Law of Sines to Solve Oblique Triangles (AAS or ASA)
 * Video: Use the Law of Sines to Solve Oblique Triangles (SSA)
 * Simulation: Law of Sines

**Objectives**
You will be able to understand the proof of the Law of Cosines and will be able to use the formula to solve a variety of problems. You will know Heron's formula and be able to use it to find areas of triangles and to solve appropriate application problems.
 * Key Ideas**

Dihedral angle Heron's formula Law of Cosines
 * Video: Use the Law of Cosines to Solve Oblique Triangles (SSS or SAS)
 * Simulation: Law of Cosines