Chapter 7

Joshua RichardsonCatherine EvansNathaniel Varner

The Trig Identities!

The Trig IDs, con’t

The Trig IDs, con’t some more

• Pythagorean Identities:

Addition and Subtraction Formulas!

Using Trig Identities…

• Write in terms of sine and cosine.

• Simplify.

t

ttsin

cossin

tt cotsin

tcos

Double Angle Formulas

Half Angle Formulas

example

Inverse Trig Functions

• If f is a one-to-one function (meaning it passes the line test) with domain (x axis) A and range (y axis) B, then its inverse f-

1is the function with domain B and range A defined by

• f -1(x) = y f(y) = x• sin-1(1) = 90o sin(90) = 1• On and graph, the inverse of a function

is flipped across the x axis.

Trig Equations

• To solve a trig equation, use the rules of algebra to isolate the trig function on one side of the equal sign. Then we use our knowledge of the values of the trig functions to solve for the variable. Other skills that are useful when solving equations include: factoring, using the inverse, and changing the angle (double or half).

examples

Trig Form of Complex numbers

• Form: a + bi when graphing instead of using an x versus y plane, use an x versus i plane.

• The modulus is defined by x = a2+b2

Vectors

• Separate into components and solve

• If a vector v is represented in the plane with initial point P(x,y) and terminal point Q(a,b), then V = (a-x, b-y)

• You find the magnitude with:

22 bav

Algebra and Vectors

• u+v=(a1+a2,b1+b2)

• With subtraction use the same formula with minuses. The same goes for multiplication.

• Most algebra is used the same way as with linear equations, just remember to apply to all components of the vector.

Components of Vectors

• Where v=(a,b)

• a=vcosanda=vsin

If and

Are vectors, then their dot product, denoted by u●v, is defined by

Dot Product and Work

),( 11 bau ),( 22 bav

2121 bbaavu Work W done by a force F is moving alona a vector D is

DFW

examples