trig functions (y2)

reciprocal trigonometric functions

-secx = 1/cosx

cosecx = 1/sinx

cotx = 1/tanx

reciprocal trigonometric functions tips and rules

-cotx = cosx/sinx as tanx = sinx/cosx

-they are undefined when the denominator is 0

-the third letter of each is the first letter of the corresponding trig function

graphing y = secx

graphing y = cosecx

graphing y = cotx

trigonometric identities

sin^2x + cos^2x = 1 derives:

1 + cot^2x = cosec^2x

1 + tan^2x = sec^2x

proving 1 + cot^2x = cosec^2x

sin^2x + cos^2x = 1

sin^2x/sin^2x + cos^2x/sin^2x = 1/sin^2x

1 + cot^2x = cosex^2x

proving 1 + tan^2x = sec^2x

sin^2x + cos^2x = 1

sin^2x/cos^2x + cos^2x/cos^2x = 1/cos^2x

tan^2x + 1 = sec^2x

arc

the inverse of a trigonometric function

(take the function and reflect it in the line y=x)

arcsin(x) = sin^-1(x) etc

inverse trig functions

trig functions aren't one-to-one, but if their domain is restricted (between + and - 𝜋/2 aka 90°) to make them one-to-one inverse functions can be defined