Formulas Flashcards
What is the formula to find a term in an arithmetic sequence?
Un= a + (n-1)d
What is the formula to find a term in a geometric sequence?
Sn= a x r^(n-1)
What is the identity equal to sin(2x) and how to you derive it?
Sin(2x)=2 x sin(x) x cos(x)
Take the sin double angle formula and substitute in x for both A and B
What are the three identities equal to cos(2x) and how do you derive them?
Substitute in x for both A and B into the cos double angle formula
Cos(2x)= cos^2(x) - sin^2(x)
Then substitute in 1-sin^2(x) for cos^2(x)
Cos(2x)= 1- 2sin^2(x)
Or substitute in 1-cos^2(x) for sin^2(x)
Cos(2x)= 2cos^2(x) - 1
What is the identity that is equal to cos^2(x) and how do you derive it?
Cos^2(x)=1/2 (1 + cos(2x))
Take cos(2x)= 2cos^2(x) - 1 and rearrange
What is the identity that is equal to 1?
1= sin^2(x) + cos^2(x)
What is the identity equal to sec^2(x) and how do you derive it?
Sec^2(x)= 1 + tan^2(x)
Take 1= sin^2(x) + cos^2(x) and divide by cos^2(x)
What is the identity equal to cosec^2(x) and how do you derive it?
Cosec^2(x)= cot^2(x) + 1
Take 1= sin^2(x) + cos^2(x) and divide by sin^2(x)
What is the formula for arc length in radians?
Arc length= Radius x theta
Arc length= r x θ
What is the formula for area of sector in radians?
Area of sector= 1/2 (radius squared x theta)
Sector area= 1/2 (r^2 x θ)
What is the formula for arc length in degrees?
Arc length= pi x radius squared x (theta/360)
Arc length = π x r^2 x (θ/360)
What is the formula for area of sector in degrees?
Area of sector= 2 x pie x radius squared x (theta/360)
Area of sector= 2 x π x r^2 x (θ/360)
What is the formula for the area of a circle?
A= π x r^2
Area= pi x radius squared
What is the formula for the circumference of a circle?
C= 2 π r
Circumference= 2 x pi x radius
What is the formula for the volume of a sphere?
V= 4/3 π r^3
Volume = 4/3 x pi x radius cubed
