Question

Hi guys! Does it make sense to make a composition of functions out of trig functions not their inverses
like \(cos(sin(x))\) since the inside function is taking angles to give ratios cos will take those ratios
does that have some sense?

Answer 1

@hartnn

Answer 2

sure

sin x is a ratio
consider that as an angle in radians

if sin x = 1/2

then cos (0.5 radians)

Answer 3

x is radians or degrees
so it is okay the consider the output of inside function as radians

Answer 4

is it?

Answer 5

i just wondered since i was reviewing my stuff about trig composition and their domains

Answer 6

the output of sin (x) is not radians, its just a pure number. the input of sine is radians (or degrees)

Answer 7

both should be same
if x is in radians, then sin x is considered in radians
if x is in degrees, then sin x is considered in degrees

Answer 8

the output of cos x or sin x is a number between -1 and 1 , think of a unit circle

Answer 9

yeah that's what i'm saying perl? it is legit to take that pure number and find it's cosine or sine for example
sine and cosine are taking angles to give ratios so i was trying to reconstruct my knowledge in this

Answer 10

yes , since the domain of cos and sine is any real number. so surely it can take an input of a number between -1 and 1

Answer 11

i know it the outputs are btw -1 and 1 (the ratios)
but is it acceptable to form such composition

Answer 12

okay i see the point here
thanks guys

Answer 13

the only problem will occur when you take composition of inverse trig functions