Precal/Trig
Standard form of the equation of a circle
(x-h)^2 + (y-k)^2 = r^2
X-axis radians
0, pi, and 2pi
Simplify sq root 2/ sq root 10
1/ sq root 5
Simplify sq root 3/ sq root 24
1/2 sq root 2
Simply 1/sq root 24
1/2 sq root 6
Simplify 3/sq root 63
1/sq root 7
sec t =
1/x, x cannot equal 0
csc t =
1/y, y cannot equal 0
Quadrant 2 degrees
120*, 135*, 150*
Quadrant 3 degrees
210*, 225*, 240*
Quadrant 2 radians
2pi/3, 3pi/4, 5pi/6
Quadrant 1 degrees
30*, 45*, 60*
Quadrant 4 degrees
300*, 315*, 330*
Quadrant 4 radians
5pi/3, 7pi/4, 11pi/6
Simplify sq root 72/ 5
6sq root 2/5
Simplify sq root 98/ sq root 2
7
Quadrant 3 radians
7pi/6, 5pi/4, 4pi/3
Area of a sector of a circle
A=1/2(theta)r^2
An area of a circle is
A=pi•r^2
Formula for circumference of a circle
C = 2πr
Simplify 3/sq root 3
Can't already simplified
Simplify sq root 3/ sq root 10
Can't already simplified
Simplify 5/sq root 21
Can't, already simplified
Simply 1/sq root 2
Can't, already simplified
Y-axis radians
Pi/2 and 3pi/2
Quadrant 1 radians
Pi/6, pi/4, pi/3
To find the length of an arc
S=r(theta) Remember that this only valid if the angle, theta, is in radians
Pythagorean identities
Sin^2t + cos^2t = 1 1 + tan^2t = sec^2t 1 + cot^2t= csc^2t
Sin t is equal to
Y
Convert radians to degrees
multiply by 180/πradians
Convert from degrees to radians
multiply by πradians/180*
Reciprocal identities
sin t = 1/csc t cos t = 1/sec t tan t = 1/cot t csc t = 1/sin t sec t = 1/cos t cot t = 1/tan t
The quotient identities
tan t = sin t/cos t cot t = cos t/ sin t
cos t =
x
cot t =
x/y, y cannot equal 0
Standard form of the equation for a unit circle
x^2 + y^2=1
tan t =
y/x, x cannot equal 0
