Chapters 6-8: Trigonometric Functions

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Chapters 6-8: Trigonometric Functions

Chapters 6,7,8:

Trigonometric functions

Chapter 7 Analytic Trigonometry

Sum & Difference Formula and its derivatives

The derivatives of Sum-Difference are: Double-Angle and Half-Angle formulas Product to sum/sum to product formulas

Used to solve and prove angles of Trig functions and their inverses

The four Trigonometric Identities

Quotient Identities Reciprocal Identities Even-Odd Identities Pythagorean Identities

Used to Prove and Solve trigonometric equations

arcsin arccos arctan arcsec arccsc arccot

Shows us the inverse of the 6 trigonometric functions

Chapter 8 Applications of Trig functions

Triangles And Right Triangles

Law of Sines And Cosines can be used solve for the sides and angles of triangles

Area Of a Triangle

Area of a triangle can be found 3 ways

For a SAS triangle

For a SSS triangle

Requires Heron's Formula to be solved.

When the Base and height are present

Law of Cosines used on: SSS Triangles SAS Triangles

Law of Sines used on: SSA Triangles ASA Triangles SAA Triangles

How it all Comes together.

The Graphs and Triangles used throughout these 3 sections are used in everyday life, such as graphing waves, finding the angles of slopes and arches, and nautical travel.

Many of the Trigonometric Equations Used to find angles will need their inverses found to get the correct angles need for their solutions

Many of the formulas and equations in Ch7 and 8 can't be done with a understanding of the unit circle and your 6 trig functions

Chapter 6: Trigonometric Function, Graphs & and the Unit circle

The 6 Trig Functions

Can be used to find the angle of two rays from their initial side to their terminal side.

Graphs of the functions look like waves

Uses the Unit circle to show Degrees & Radians

Sine/sin Cosine/cos Tangent/tan Secant/sec Cosecant/csc Cotangent/cot