Exam 3 Review Flashcards
Memorize what's necessary
What is sin(theta) also equal to?
1/csc(theta)
What is cos(theta) also equal to?
1/sec(theta)
What is tan(theta) also equal to?
1/cot(theta)
What is csc(theta) also equal to?
1/sin(theta)
what is sec(theta) also equal to?
1/cos(theta)
what is cot(theta) also equal to?
1/tan(theta)
What is the fundamental Pythagorean identity?
sin^2(x)+cos^2(x)=1
How can you express cos^2(x) in terms of sin^2(x)?
cos^2(x) = 1- sin^2(x)
How can you express sin^2(x) in terms of cos^2(x)?
sin^2(x) = 1- cos^2(x)
How can you express sec^2(x) in terms of tan^2(x)?
sec^2(x) = 1+ tan^2(x)
How can you express csc^2(x) in terms of cot^2(x)?
csc^2(x) = 1+ cot^2(x)
How can you express tan^2(x) in terms of sec^2(x)?
tan^2(x)= sec^2(x) - 1
How can you express 1 in terms of tan^2(x) and sec^2(x)?
1= sec^2(x) - tan^2(x)
How can you express cot^2(x) in terms of csc^2(x)?
cot^2(x)= csc^2(x) -1
How can you express 1 in terms of csc^2(x) and cot^2(x)?
1= csc^2(x) - cot^2(x)
What is the formula for converting from radians to degrees?
Radians = 180/pi degrees
What is the formula for converting from degrees to radians?
Degrees = pi/180
What is the formula for arc length?
S = r*theta
How do you find the linear velocity of a circle?
You set velocity = to r*w and convert w with 2pi then balance the answer to the desired unit.
What is the even identity for cosine?
cos(−x)= cos(x)
What is the odd identity for sine?
sin(−x)= −sin(x)
What is the odd identity for tangent?
tan(−x)= −tan(x)
What is the even identity for secant?
sec(−x)= sec(x)
What is the odd identity for cosecant?
csc(−x)= −csc(x)
What is the sum identity for sine?
sin(A+B) =sin(A)cos(B)+cos(A)sin(B)
What is the odd identity for cotangent?
cot(−x)= −cot(x)
What is the sum identity for tangent?
tan(A+B) =tan(A)+tan(B)/1−tan(A)tan(B)
What is the difference identity for sine?
sin(A−B) =sin(A)cos(B)−cos(A)sin(B)
What is the sum identity for cosine?
cos(A+B) =cos(A)cos(B)−sin(A)sin(B)
What is the difference identity for cosine?
cos(A−B) =cos(A)cos(B)+sin(A)sin(B)
What is the difference identity for tangent?
tan(A−B) =tan(A)-tan(B)/1+tan(A)tan(B)
What is the double-angle identity for sine?
sin(2x) =2sin(x)cos(x)
What is the double-angle identity for cosine?
cos(2x) =cos^2(x)-sin^2(x), cos(2x) =2cos^2(x)-1, 1-2sin^2(x)
What is the double-angle identity for tangent?
tan(2x) =2tan(x)/1−tan^2(x)
What is the power-reduction identity for sin^2(x)?
sin^2(x)= 1−cos(2x)/2
What is the power-reduction identity for cos^2(x)?
cos^2(x) =1+cos(2x)/2
What is the power-reduction identity for tan^2(x)?
1−cos(2x)/1+cos(2x)
What is the domain and range of sin(x)?
D: (-infinity,infinity) R:[-1,1]
What is the domain and range of cos(x)?
D:(-infinity,infinity) R:[-1,1]
What is the domain and range of tan(x)?
D:{t|t=\ pi/2 + pik} R:(-infinity,infinity)
What is the domain and range of csc(x)?
D:{t|t=\ pik, k any integer} R:(-infinity,-1]U[1,infinity)
What is the domain and range of sec(x)?
D:{t=\ pi/2+pik, k is any integer} R:(-infinity,-1]U[1,infinity)
What is the domain and range of cot(x)?
D:{t=\ kpi, k is any integer} R:(-infinity,inifinity)
What is the domain and range of arcsin(x)?
D:[-1,1] R:[-pi/2,pi/2]
What is the domain and range of arccos(x)?
D:[-1,1] R:[0,pi]
What is the domain and range of arctan(x)?
D:(-infinity,infinity) R:(-pi/2,pi/2)
What is the domain and range of arccsc(x)?
D:(-inifinity,-1]U[1,infinity) R:[-pi/2,pi/2],y=\0
What is the domain and range of arcsec(x)?
D:(-infinity,-1]U[1,infinity) R:[0,pi],y=\pi/2
What is the domain and range of arccot(x)?
D:(-infinity,infinity) R:(0,pi)
