Gr 10 Equations Review Flashcards
What is the equation for SOH
sin= opp/hyp
What is the equation for CAH
cos= adj/hyp
What’s the equation for TOA
tan= opp/adj
What’s the equation for similar triangles?
AB AC BC
— = — = —
DE DF EF
What’s the equation for sin law?
a b c
______ = ______= ______
Sin A Sin B Sin C
What’s the equation for cosine law pt 1 side lengths
2 2 2
b = a + c - 2ac(cos B)
What’s the equation for cosine law pt 2 angles
2 2 2
b = a + c - 2ac(cos B)
(move all numbers to left side of equal sign to isolate cos B)
What do you get in standard form?
- y-int
- step 1, 3, 5
- direction of opening
What do you get from vertex form?
- vertex (h,k)
- aos (x=h)
- step 1, 3, 5
- direction of opening
What do you get from factored form?
- x-ints/roots (r, s)
- step 1, 3, 5
- direction of opening
What is standard form?
2
y= ax + bx + c
What is vertex form?
2
y= a (x-h) + k
What is factored form?
y= a (x-r) (x-s)
What is the equation for the shortcut from standard to vertex form?
-b
x = ——
2a
What is the equation of a line?
y = mx + b
What’s the equation for the midpoint of a line?
X1 + X2 Y1 + Y2
M = ( ———— ———— )
2 , 2
What’s the equation for the slope of a line?
Y2 - Y1
m = ————
X2 - X1
What’s the equation for a circle centered at the origin?
2 2 2
x + y = r
What’s the equation for a circle not centered at the origin?
2 2 2
( x - h ) + ( y - k ) = r
What’s the equation for the length of a line?
____________________
L = / 2 2
\/ (X2 - X1) + (Y2 - Y1)
What’s the equation for quadratic formula?
___________
+ / 2
X = - b - \/ b - 4ac
——————————
2a
When do you use sin law?
If it isn’t a 90* angle and there is a complete side / angle pair
When do you use soh cah toa?
When it is a 90* angle
When do you use cosine law pt. 1 side lengths
When you have two sides and an angle
When do you use cosine law pt. 2 angles
when you have three sides of the triangle
How many roots if it is
2
b - 4ac > 0
2 real roots
How many roots if it is
2
b - 4ac = 0
2 equal roots
How many roots if it is
2
b - 4ac < 0
0 real roots
