Trig. Identities
If cos x = (2/3) find sec x.
What is sec x = (1/cos x)
=(1/(2/3))
=(3/2)
sec2x(1 - cos2x)
sec2x(1 - cos2x)
= sec2x - (sec2x)(cos2x)
= sec2x - (1/cos2x)(cos2x)
= sec2x - 1
= tan2x
Find all the solutions in degrees between 0 and 360:
4=-8cos(x)
-1/2 = cos x
x = 120 and 240
Solve for all angles between 0 and 2pi.
5sin x+2=sin x
5sinx+2 = sin x
4sinx+2=0
2(2sinx+1)=0
2sinx = -1
sin x = (1/2)
x = 7pi/6 and 11pi/6
This island is the largest in the Continental U.S.
What is Long Island? Snapple Fact #333
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)
(cot2x)(csc2x) - cot2x = cot4x
(cot2x)(csc2x) - cot2x
= (cot2x)(csc2x - 1)
= (cot2x)(cot2x)
= cot4x
Find all the solutions on the unit circle in degrees between 0 and 360:
5=1+2csc(x)
5 = 1 + 2csc(x)
4 = 2csc(x)
2 = csc(x)
1/2 = sin(x)
x = 30 and 150
Find all solution on the unit circle between 0 and 2pi.
cot x = sqrt(3)
cot x = sqrt(3)
tan x = 1/sqrt(3)
tan x = sqrt(3)/3
x = pi/6, 7pi/6
This letter was the last letter to be added to the English alphabet
What is J? Snapple Fact #336
If csc x = sqrt(15)/3, find sin x exactly.
csc x = 1/sinx
1/sin x = sqrt(15)/3
sin x = 3/sqrt(15) = sqrt(15)/5
How is the verification of identities different than solving trig equations?
Verification you are working with one side to manipulate it to look like the other side.
Solving equations you are still kind of manipulating but you can work with both sides, and there are specific answers you are looking for.
PICK A NUMBER (between 0 and 1000)
Lose that many points.
Find all solutions for x.
2-10secx=4-9secx
2-10secx = 4-9secx
-10secx = 2-9secx
-secx = 2
secx = -2
cosx = -(1/2)
x = 2pi/3 + 2npi, 4pi/3 + 2npi, n = int.
This aquatic mammal sleeps with one eye open
What is a dolphin? Snapple Fact #760
The exact value of sin(240o).
sqrt(3) / 2
PICK A NUMBER (Between 0-1000)
Gain that many points
Find all radian solutions [0,2pi) of
2cos2x + cosx - 1 = 0
(2cosx + 1)(cosx - 1) = 0
2cosx + 1 = 0 and cosx - 1 = 0
cosx = -1/2 and cosx = 1
x = 2pi/3, 5pi/3, 0, pi
Find all solutions for x.
3cscx = 2cscx+(√2)
3cscx = 2cscx+(√2)
cscx = (√2)
sinx = (1/(√2))*((√2)/(√2))
sinx = (√2)/2)
x = pi/4 +2npi, 3pi/4 + 2npi, n = int.
This slow and slimy animal has four noses.
What is a slug?
Snapple fact #3.
If the exact value of cos(x) is 5/7, and tan x < 0, find all five other trig ratios exactly.
sin x = -2sqrt(6)/7
sec x = 7/5
csc x = -7sqrt(6)/12
tan x = -2sqrt(6)/5
cot x = -5sqrt(6)12
csc x sec x - tan x
csc x sec x - tan x
= (1/sinx)*(1/cosx) - (sinx/cosx)
= 1/(sinxcosx) - (sinx/cosx)
= 1/(sinxcosx) - sin2x/(sinxcosx)
= (1-sin2x)/(sinxcosx)
= (cos2x)/(sinxcosx)
= (cosx/sinx)
= cotx
Solve for all angles between 0 and 2pi:
(cos x)(sin x) - (sin x) = 0
(sin x)(cos x - 1) = 0
sin x = 0 and cos x - 1 =0
x = 0, pi and x = pi/2
Find all solutions for x.
11=3csc2x+7
11=3csc2x+7
4=3csc2x
(4/3) = csc2x
(+/-)((√(4/3))=(√csc2x)
csc x = (+/-)(2/(√3))or(+/-)(2(√3)/3)
sin x=(+/-)(√3/2)
x = (pi/3), (2pi/3), (4pi/3), (5pi/3) all + 2npi, n = int.
This is Barbie's full name
What is Barbara Millicent Roberts? Snapple Fact #902