Reciprocal/Quotient Identities
The reciprocal of sin
What is csc?
sin²x + cos²x
What is 1?
sec2x(1-cos2x)
What is sec2x(1-cos2x)
=sec2x-sec2xcos2x Distributive Property
=sec2x-(1/(cos2x))*cos2x Reciprocal Identity
=sec2x-1 Multiply and divide out common factor
=tan2x Pythagorean Identity
Tips for solving trig identities?
What are.....
-convert to sines and cosines
-work on one side only
-start with more complicated side
-Factoring, adding or subtracting fractions, simplifying complex fractions
-Use basic fundamental identities
Find the solutions in degrees:
4=-8cos(x)
120 and 240
The year that Northwest HS opened.
What is 1975?
The quotient of "cos/sin"
What is cot?
1 - cos²x
What is sin²x?
cot2x csc2x-cot2x
What is cot2xcsc2x-cot2x
=cot2(csc2x-1) Factor
=cot2xcot2x Pythagorean Identity
=cot4x Multiply and add exponents
PICK A NUMBER (Between 0-1000)
Lose that many points
Find the solutions in degrees:
5=1+2csc(x)
30 and 150
PHONE A FRIEND to name 3 historical landmarks in and around Dalton, GA. (Split the points)
What are:
Prater’s Mill
Western & Atlantic Railroad Tunnel
Hamilton House
New Echota
Red Clay--Cherokee Council Grounds
Dalton Confederate Cemetary
Chief Vann House
Dalton Freight Depot and Train Viewing Platform
The reciprocal of sec.
What is cos?
PASS GO
Gain 500 points
sin x (csc x - sec x)
What is 1 - tan x?
Verify:
cot2x = csc2x - cosxsecx
cot2x = csc2x - cosxsecx
cot2x = csc2x - 1
cot2x = cot2x
All radian solutions [0,2pi) of 2cos2x + cosx - 1 = 0
What are pi/3, 5pi/3, and pi?
Who's grave is on top of the ridge behind the First Church of The Nazarene and the State Patrol Barracks in Rocky Face, GA.
Who is George W. Disney?
If cos x = (2/3) find sec x.
What is sec x = (1/cos x)
=(1/(2/3))
=(3/2)
sec²x - 1
What is tan²x?
BANKRUPT
Lose all your points
cos2x = 1/(1-sin2x) - cot2x - 2(1-cos2x)
cos2x = 1/(1-sin2x) - cot2x - 2(1-cos2x)
cos2x = 1/(cos2x) - cot2x - 2(1-cos2x)
cos2x = csc2x - cot2x - 2(1-cos2x)
cos2x = 1 - 2(1-cos2x)
cos2x = 1 - 2sin2x
cos2x = cos2x
The exact value of sin(2x) if cosx = 1/4 and x is in quadrant 4.
What is (- sqrt 15)/8 ?
The bird is most associated with Dalton GA.
What is the peacock?
If cos x = (1/6) and sin x = ((√35)/6) find cot x
What is cot x = ((cos x)/(sin x))
=((1/6)/(√35)/6)
=(1/(√35)) * ((√35)/(√35))
=((√35)/35)
(1 + csc x)(1 - csc x)
What is -cot²x ?
csc x sec x - tan x
What is csc x sec x - tan x = (1/sinx)*(1/sinx)-(sinx/cosx)
=(1/(sinxcosx))-(sinx/cosx)
=(1/(sinxcosx))-(sinx/cosx)
=(1/(sinxcosx))-(sinx/cosx)(sinx/sinx)
=((1-sin2x)/(sinxcosx)
=((cos2x)/(sinxcosx)
=(cosx/sinx)
=cotx
sin(2+2x) = sin2cos2x - sin2sin2x + 2cos2sinxcosx
sin(2+2x) = sin2cos2x - sin2sin2x + 2cos2sinxcosx
sin(2+2x) = sin2(cos2x-sin2x) + cos2(2sinxcosx)
sin(2+2x) = sin2(cos2x-sin2x) + cos2sin2x sin(2+2x) = sin2cos2x + cos2sin2x
sin(2+2x) = sin(2+2x)
PICK A NUMBER (Between 0-1000)
Gain that many points
The name of the summer concert series held downtown GA.
What is Off The Rails?