Unit Circle
Circumference of a circle
2πr
270 degrees
3π/2 radians, -1 sin, 0 cosine, tan und, csc -1, secant und, cot 0
to do those hard word problems
s = thêta x r (find degrees in radians) theta (in radians)= s/r
60 degrees in radians
π/3
60 degrees
π/3 radians, SR 3/2, cos 1/2, SR 3, csc 2 SR 3/3, sec 2, cot SR 3/3
Area of a sector of a circle if given an angle measure if given a degree
A = 1/2 r^2 θ divide by 60 and 3600 x60
determine the quadrant in which the terminal side of each angle lays 17 pi/ 4 -789 degrees Find the degree measure for a 7/16 rotation clockwise
a.) 1 b.) 4 -157.5
each degree has each minute has
60 minutes (60') 60 seconds (60'')
sine, cosine, tangent
opp/hyp, adj/hyp, opp/adj
90 degrees
π/2 radians, sin 1, cos 0, tan und, csc 1, sec und, cot 0
45 degrees
π/4 radians, sin SR2/2, cos SR 2/2, tan 1, csc SR 2, sec SR 2, cot 1
0 degrees
0 radians, sine 0, cosine 1, tan 0, coscecant und, secant 1, cotangent und
330 degrees
11π/6 (√3/2 cosine, -1/2 sine, tan - SR 3/3, csc -2, secant 2 SR 3/3, cot - SR 3
360 degrees
2π radians, sin 0, cos 1, tan 0, csc und, sec 1, cot und
120 degrees
2π/3 radians, (-1/2 cosine, √3/2 sine, -SR 3 tangent, csc 2 SR 3/3, sec -2, cot -SR 3/3)
135 degrees
3π/4 radians, (-√2/2 cosine, √2/2 sine, tan 1, csc SR 2, secant -SR 2, cot-1)
240 degrees
4π/3 radians, (-1/2 cos, -√3/2 sine, tan SR 3, csc -2 SR 3/3, sec -3, cot SR 3/3
1 radian = ____ degrees
57.3 degrees
300 degrees
5π/3 radians, (1/2 cosine, -√3/2 sine, tan - SR 3, csc -2 SR 3/3, sec 2, cot - SR 3/3
225 degrees
5π/4 radians, (-√2/2 cosine, -√2/2 sine, tan 1, csc - SR 2, secant - SR 2, cot 1
150 degrees
5π/6 radians, (-√3/2 cosine, 1/2 sine, tan -SR 3/3, csc 2, secant -2 SR 3/3, cot - SR 3)
315 degrees
7π/4 radians, (√2/2 cosine, -√2/2 sine, tan -1, csc - SR 2, secant SR 2, cot -1
210 degrees
7π/6 radians, (-√3/2 cosine, -1/2 sine, tan SR 3/3, csc -2, secant -2 SR3/3, cot SR 3)
theta
A Greek symbol commonly used to represent an unknown angle
theta =
S-R and 2 radians
Helpful to remember sine cos and tan sin = Cosine = tan = 1/2 revolution ... 1/4 revolution 1/6 revolution one degree = ____ rotation
SOH CAH TOA 1/ csc (recip) 1/ sec 1/cot pi radians pi/2 radians pi/3 radians 1/360 rotation l
linear speed = angular speed = s=
arc length / time (how fast particle moves) s/t central angle (in radians)/time (how fast angle changes) so theta / t 2pi(r) (arc length =)
where does everything go on unit circle? the circumference of a circle is 1/2 revolution = ___ radians 1/4 revolution = 1/6 revolution =
circle is degree, big box is radians, coordinates are cosine (x) and sine (y) 2 pi pi pi/2 radians pi/3 radians
To find coterminal angles
subtract 2pi or add 2pi - is positive subtract two pi, if negative add two pi
complementary if supplementary if 1 degree = 1 radian = degrees to radians radians to degrees
sum is pi/2 sum is pi pi/180 radians 180/ pi degrees multiply by pi radians/ 180 multiply by 180/ pi radian
sine is cosine is tangent is cosecant is secant is cotangent
y odd sin (-x) = - sin x. even cos (-x) = cos y/x odd tan (-x) = -tan 1/y odd csc (-x) = -csc 1/x even sec (-x) = sec x/y odd cot (-x) = -cot
180 degrees
π radians, sin 0, cos -1, tan 0, csc und, sec -1, cot und
30 degrees
π/6 radians, sine 1/2, cos square root 3/2, tan square root 3/3, csc 2, sec 2 squareroot of 3/3, cot square root of 3
