Mathematics Chap 27

Chap 27, 27A to F

P

( cos theta, sin theta )

x coordinate

cos theta

y coordinate

sin theta

0 ~ 90

A ( all positive )

90 ~ 180

S ( sin positive )

180 ~ 270

T ( tan positive )

270 ~ 360

C ( cos positive )

negative 90

quarter turn clockwise ( 360 - angle )

cos ( - theta )

cos theta

sin ( - theta )

- sin theta

tan ( - theta )

- tan theta

cos ( 180 + theta )

- cos theta

sin ( 180 + theta )

- sin theta

tan ( 180 + theta )

tan theta

cos ( 180 - theta )

- cos theta

sin ( 180 - theta )

sin theta

tan ( 180 - theta )

- tan theta

cos ( 360 + theta )

cos theta

sin ( 360 + theta )

sin theta

tan ( 360 + theta )

tan theta

cos ( 360 - theta )

cos theta

sin ( 360 - theta )

- sin theta

tan ( 360 - theta )

- tan theta

sin ( 0 )

0

cos ( 0 )

1

tan ( 0 )

0

sin ( 30 )

1/2

cos ( 30 )

(root 3)/2

tan ( 30 )

1/(root 3)

sin ( 45 )

1/(root 2)

cos ( 45 )

1/(root 2)

tan ( 45 )

1

sin ( 60 )

(root 3)/2

cos ( 60 )

1/2

tan ( 60 )

root 3

sin ( 90 )

1

cos ( 90 )

0

tan ( 90 )

undefined

cos²theta + sin²theta

1

y = a sin bx + d ( a )

amplitude |a| ( a<0 flips it )

y = a sin bx + d ( b )

period = 360/b

y = a sin bx + d ( d )

principal axis y = d

a

maximum point

b

amplitude

c

period ( one full cycle )

d

minimum point

e

principle axis

pi rad

180 degrees

Degree Conversion

Radians: multiply by pi/180

Radian Conversion

Degrees: Multiply by 180/pi

30 degrees

pi/6

45 degrees

pi/4

60 degrees

pi/3

90 degrees

pi/2

135

3pi/4

180 degrees

pi

210 degrees

7pi/6

240 degrees

4pi/3

300 degrees

5pi/3

330 degrees

11pi/6

Fraction of circle

theta/2pi

Arc length of circle

1 = theta/2pi x 2pir (theta must be in radians)

r

Radius of a circle

Shape

Segment

Shape

Triangle

Shape

Sector

Arc length

l = r(theta)

Area of a sector 1

1/2r²(theta)

Area of a sector 2

1/2rl

Isosceles triangle area

1/2r²sin(theta)

Segment area

1/2r²(theta-sin(theta)) or sector - triangle