Graphics - Trig Summary

trigonometry

measurement of triangles

2pi

the radians that make up a full circle

360

the degrees that make up a full circle

radians

a number without a notation but referring to an angle is assumed to be in

degrees

° is the symbol for

180/pi

multiply this by a radian to get a degree

pi/180

multiply this by a degree to get a radian

T

T/F angles are measured from the positive side with counter-clockwise being positive angle measurement

are not

The axis (are/are not) included in the quadrants

1

what is the radius of the unit circle

30

the angle with cos = sqrt(3)/2 and

sin = 1/2

45

the angle with cos, sin = sqrt(2)/2

60

the angle with cos = 1/2 and sin = sqrt(3)/2

90

the angle with cos = 0 and sin = 1

0

the angle with cos = 1 and sin = 0

unique

angle measurement is not ____________

they are congruent with any other angle 360\* values greater than or less than it

principal value

the value of an angle that falls betweens -180 and 180 degrees (two words)

cos

the x component of the spot where the hypotenuse touches the unit circle

sin

the y component of the spot where the hypotenuse touches the unit circle

2pi

what is the period of sin and cos

1

sin^2(Θ) + cos^2(Θ) =

do

cos and sin (do/do not) repeat values if the interval is \[0,2pi\]

odd

sin is and ______ function, meaning it is symmetric about the origin

even

cos is and _______ function, meaning is is symmetric about the y axis

sin(Θ+Φ)

sinΘcosΦ + cosΘsinΦ =

cos(Θ+Φ)

cosΘcosΦ - sinΘsinΦ =

sin(Θ-Φ)

sinΘcosΦ - cosΘsinΦ =

cos(Θ-Φ)

cosΘcosΦ + sinΘsinΦ

1

the Limit of sinΘ/Θ as Θ→0

cosΘ

d/dΘ sinΘ =

\-sinΘ

d^2/d^2Θ sinΘ =

6

there are trig functions

e^(i0) = cos0 + isin0

euler’s formula (use 0 as theta)

okay

Know the law of cosines, how to derive any example of side/hypotenuse into cos(Θ+Φ) and the other formulas, as well as using eulers to derive sum-of-angles