Review of mathematic Flashcards
a+a=
2a
(a^x)(a^y)=
a^x+y
a(c+d)=
ac+ad
(a+b)(a+b)=
a^2+ab+ab+b^2=
a^2+2ab+b^2
(a+b)^2=
(a+b)(a+b)=
a^2+ab+ab+b^2=
a^2+2ab+b^2
(a-b)^2=
(a-b)(a-b)=
a^2-2ab+b
(a+b)(a-b)=
a^2-b^2
(a^x)^y=
a^x∙y
(ab)^x=
a^x∙b^x
(a/b)^x=
(a^x) / (b^x)
a^0=
1
(a^x) / (a^y)=
a^x-y
a^-x=
1 / a^x
(a/b) + (c/b)=
(a+c) / b
(a/b) + (c/d)=
(ad)/(bd) + (cb)/(bd)=
(ad + bc) / bd
(a/b) - (c/b)=
(a-c) / b
(a/b) - (c/d)=
(ad)/(bd) - (cb)/(bd)=
(ad - bc) / bd
(a/b)(c/d)=
(ac) / (bd)
(a/b) / (c/d)=
(ad) / (bc)
30 degrees
π/6
45 degrees
π/4
60 degrees
π/3
90 degrees
π/2
120 degrees
2π/3
135 degrees
3π/4
150 degrees
5π/6
180 degrees
π
210 degrees
7π/6
225 degrees
5π/4
240 degrees
4π/3
270 degrees
3π/2
300 degrees
5π/3
315 degrees
7π/4
330 degrees
11π/6
360 degrees
2π
What is the formula to find the arc length?
s=rθ where θ is in radian
(x,y) points of the angle π/6
√3/2, 1/2
(x,y) points of the angle π/4
√2/2, √2/2
(x,y) points of the angle π/3
1/2, √3/2
(x,y) points of the angle π/2
0, 1
(x,y) points of the angle 2π/3
-1/2, √3/2
(x,y) points of the angle 3π/4
-√2/2, √2/2
(x,y) points of the angle 5π/6
-√3/2, 1/2
(x,y) points of the angle π
-1, 0
(x,y) points of the angle 7π/6
-√3/2, -1/2
(x,y) points of the angle 5π/4
-√2/2, -√2/2
(x,y) points of the angle 4π/3
-1/2, -√3/2
(x,y) points of the angle 3π/2
0, -1
(x,y) points of the angle 5π/3
1/2, -√3/2
(x,y) points of the angle 7π/4
√2/2, -√2/2
(x,y) points of the angle 11π/6
√3/2, -1/2
(x,y) points of the angle 2π
1, 0
(x,y) points of the angle 0
1,0
The inverse of Sin is
Csc
The inverse of Cos is
Sec
The inverse of Tan is
Cot
inverse identity cscθ=
1 / sinθ
inverse identity sinθ=
1/ cscθ
inverse identity secθ=
1/ cosθ
inverse identity cosθ=
1/ secθ
inverse identity cotθ=
1/tanθ
inverse identity tanθ=
1/cotθ
quotient identity tanθ=
sinθ / cosθ
quotient identity cotθ=
cosθ / sinθ
Pythagorean identity sin^2θ + cos^2θ=
1
Pythagorean identity 1+tan^2θ=
sec^2θ
Pythagorean identity 1+cot^2θ=
csc^2θ
negative identity -sinθ=
sin(-θ)
negative identity -cscθ=
csc(-θ)
negative identity -tanθ=
tan (-θ)
negative identity -cotθ=
cot(-θ)
negative identity cos (-θ)=
cosθ
negative identity sec(-θ)=
secθ
opp, adj, hyp Sin=
opp / hyp
opp, adj, hyp csc=
hyp / opp
opp, adj, hyp cos=
adj / hyp
opp, adj, hyp sec=
hyp / adj
opp, adj, hyp tan=
opp / adj
opp, adj, hyp cot=
adj/ opp
Cos (a+b)=
cos(a)cos(b) - sin(a)sin(b)
Cos (a-b)=
cos(a)cos(b) + sin(a)sin(b)
cos (π/2 -θ)=
sinθ
sin (π/2 -θ)=
cosθ
sin (a+b)=
sin(a)cos(b) + cos(a)sin(b)
sin(a-b)=
sin(a)cos(b) - cos(a)sin(b)
tan (a+b)=
tan(a) + tan(b) / 1 - tan(a)tan(b)
tan (a-b)=
tan(a) - tan(b) / 1 + tan(a)tan(b)
sin2θ=
2sinθcosθ
tan2θ=
2tanθ / 1-tan^2θ
cos2θ= 3 forms
cos^2θ - sin^2θ
1 - 2sin^2θ
2cos^2θ - 1
sin (θ/2)=
± √(1 - cosθ /2)
cos(θ/2)=
± √(1 + cosθ /2)
tan (θ/2)=
± √(1 - cosθ / 1 + cosθ)
What is the formula to find the distance in a straight line?
d=√((x2- x1)^2 + (y2-y1)^2)
What is the formula to find the midpoint of a straight line?
M= (x1 + x2) /2 , (y1 - y2) /2
What is the formula of a straight line?
y=mx+b
What is the formula to find the slope of a straight line?
m= (y2-y1) / (x2-x1)
What is the general form of the equation of a circle?
x^2 + y^2 + ax + by + c=0
What is the standard form of the equation of a circle?
(x-h)^2 + (y-k)^2=r^2
What is the equation of a quadratic function?
ax^2 + bx +c
What is the standard form of a quadratic function?
a (x-h)^2 +k
What is the simple interest formula?
I=Prt
I=interest
P=principal deposite
r=rate
t=time in years
What is the compound interest formula?
A=P (1 + (r/n))^nt
A=total money r=interest rate n=number of compounding period P=initial deposite t=time
What is the formula for the continuous compound interest?
A=Pe^rt
A=total money P=initial deposite e= e in the calculator r=rate t=time in year
