Unit 4 Advanced Algebra Review
How to Read Unit Circle Coordinates
(x,y)=(cos,sin)
Negative Angle Identities
* sin (-x) = -sin x * cos (-x) - cos x * tan (-x) = -tan x
EXTRA NOTES
* sin(90)=1; sin(-90)=-1 ALSO sin(270)=-1 * sin(30)=1/2; sin(-30)=-1/2 ALSO sin(330)=-1/2 * cos(60)=1/2; cos(-60)=1/2 ALSO cos(300)=1/2 * cos(120)=-1/2; cos(-120)-1/2 ALSO cos(240)=-1/2
Trig Identities
* sin^2 + cos^2 =1 * tan =sin /cos * 1/tan =cos /sin * cos^2 =1-sin^2 * sin^2 =1-cos^2 *GOAL IS TO END WITH A SINGLE VALUE*
Trigonometry
*SOH CAH TOA*
Solving Trig Equations
*SOLVE:* the process for solving trig equations is the same as solving linear equation. You want to get the "unknown" (cos(x), sin(x), & tan(x)) on one side of the = and everything else on the other side
Verifying Trig Equations
*When verifying, you will be given an equation & the goal is to make the right side look like the left side or vice versa *Make the complicated side "look like" the simple side *ONLY CHANGE ONE SIDE* *USE TRIG IDENTITIES TO SOLVE!!!*
Phase Shift
*when a Trigonometric function moves to the left or right* LOOKS LIKE(any equation like this): y=cos(x- )
Unit Circle
A circle whose center is at the origin and has a radius of one
tan(0)=y/x
cot(0)=x/y
sin(0)=y/r
csc(0)=r/y
Degrees= Radians=
decimals fractions
Convert from Radians to Degrees:
multiply by 180*/π
Convert from Degrees to Radians:
multiply by π/180*
cos(0)=x/r
sec(0)=r/x
Reference Angle
the positive acute angle formed by the terminal side & the horizontal axis
Coterminal Angles
two angles in the standard position with the same terminal side (there are infinitely many coterminal angles) *Add or Subtract 360 to get other coterminal angle(DEGREES)* *Add or Subtract 2 to get other coterminal angle(RADIANS)*
Angle
two rays with the same endpoint make an _______
ORDER!!!!
y= -2 sin 1/2 (x- )
Changing Period
y=cos 1/2 0 OP: 2 NP: 2 /1/2 NP=4
Graphing Trig Equations
y=sin(x) *LOOK AT Y-VALUES* y=cos(x) *LOOK AT X-VALUES* y=tan(x) *DIVIDE Y-VALUE BY X-VALUE*
Tangent Values
(1/2, 3/2)= 3 ( 2/2, 2/2)= 1 ( 3/2, 1/2)= 3/3 *POSITIVE IN QUADRANTS 1&3* *NEGATIVE IN QUADRANTS 2&4*