Question

True or False: tan(arctan(b)) is always equal to b

Answer 1

hmmm what would \(\bf tan^{-1}(b)\) give us anyway? a number? an angle? what would it give us?

Answer 2

false I think tan function is not continous, it i s undefined somewhere

Answer 3

@jdoe0001 would it give us a number if we plugged something in for b

Answer 4

a number hmm ok

so that means "b" is an angle?

Answer 5

oh

Answer 6

So it would give us an angle

Answer 7

Are the functions tan and arctan inverses?

Answer 8

yeap, it gives us an angle
and so b is a number

so say for example

yes, they're inverses

Answer 9

so if they are inverses does that mean they are not equal or false?

Answer 10

so \(\bf {\color{blue}{tan^{-1}(1) }} =45^o\implies tan(45^o)=1
\\ \quad \\
tan[{\color{blue}{ tan^{-1}(1) }} ]=1\)

Answer 11

tan(arctan(b)) gives b as long as your arguments is in the contnious region

Answer 12

inverses doesn't mean they're equal in any way, no

Answer 13

the inverse tangent function, will take a number, and spit out an angle
the tangent will take an angle, and spit out a number

if the tangent, takes an angle, that was spit out by the inverse tangent
then the number that tangent will spit out, will be the same the inverse tangent took in

Answer 14

that's pretty much true for all inverse trigonometric functions
sine, cosine, tangent, cotangent, secant and cosecant

Answer 15

so \(cos[cos^{-1}(x)]=x\qquad \qquad sin[sin^{-1}(x)]=x
\\ \quad \\
csc[csc^{-1}(x)]=x\qquad \qquad sec[sec^{-1}(x)]=x
\\ \quad \\
tan[tan^{-1}(x)]=x\qquad \qquad cot[cot^{-1}(x)]=x\)

Answer 16

oh so its true then?

Answer 17

if the x is equal to x

Answer 18

yeap

Answer 19

https://www.google.com/search?q=cos%28+%5Bacos%280.906307787%5D%29&client=opera&oe=utf-8&channel=suggest&gws_rd=ssl&oq=cos%28+%5Bacos%280.906307787%5D%29&gs_l=heirloom-serp.3..19.10978.12618.0.13345.11.7.0.0.0.2.410.845.4j1j4-1.6.0....0...1ac.1.34.heirloom-serp..7.4.691.2y3YeD6UmNA

Answer 20

Oh ok thank you for your time and help :)

Answer 21

yw

Answer 22

...and explaining it to me :)