Unit Circle

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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


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