Amy's Reflection #30

Idenities and Equations...

Steps for solving:
1. check Idenities
2.Use Algebra: combining, factoring, multiplacation, fraction, and sandwiching.
3. then go back to idenities

Example:

Simplify SecX-SinX TanX

use and identity for secX and tanX
1/cosX-sinX(sinX/cosX)
distribute sinx into ( sinx/cosx)
1-sin^2X/cosX
use the iden. and solve for cos^2X with 1-sin^2X
Cos^2 X/ CosX= Cosx

And here are some things you're gonna need to know for the test...

Reciprocal Relationships:
csc (theta)=1/sin (theta)
sec (theta) =1/cos (theta)
cot (theta) =1/tan (theta)

Relationships with Negatives:
sin (-theta) = -sin (theta) and cos (-theta) = -cos (theta)
csc (-theta) = -csc (theta) and sec (-theta)= -sec (theta)
tan (-theta)= -tan (theta) and cot (-theta)= -cot (theta)

Pythagorean Relationship:
sin² (theta) + cos² (theta) =1
1+tan² (theta) = sec² (theta)
1+cot² (theta) = csc² (theta)

Cofunction Relationships
sin (theta) = cos(90°- theta) and cos (theta) = sin(90°-theta)
tan (theta) = cot(90°-theta) and cot (theta) =tan(90°-theta)
sec (theta) = csc(90°-theta) and csc (theta)=sec(90°-theta)

Cautions:

**you can't divide trig functions to cancel them

Example:

2 cos (theta) / cos (theta) = cos² (theta)/ cos (theta)

**but you can move everything to one side & factor out a trig function
**or divide by a trig function to create a new one:

Example:

sinxtanx = 3sinx

sinxtanx - 3sinx = 0

sinx (tanx - 3) = 0

sinx = 0

x = sin^-1 (0)

x = 0, pie, 2pie

tanx -3 = 0

tanx = 3

x = tan^-1 (3)

x= 71.565 pie/180, 257.565 pie/180