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Understand That Arcsine, Arccosine, And Arctangent Represent The Inverse Of A Sine, Cosine, And Tangent Function Respectively

Is the sentence true or false?
In order to have an inverse function for trigonometry, we restrict the domain of each function, so that it is one to one.

True

False

Determine either $f\left(x\right)=\sin x$ , then what is the value of $f^{-1}\left(x\right)$ ?

$\sin x$

$\arcsin x$

neither

Determine either $f\left(x\right)=x$ , then what is the value of $f^{-1}\left(x\right)$ ?

$\sin x$

$\arcsin x$

neither

Is the sentence true or false?
$arc\left(\arccos\cos x\right)=\cos\left(x\right)$ is odd function.

True

False

Complete: If $f\left(x\right)=\tan x$ , then what is the value of $f^{-1}\left(x\right)$ ?

$\cos x$

$x$

$\tan\tan x$

Is the number sentence true or false?
$\sin\left(0.5\right)=0.5$

True

False

Complete:
$\left(\sin x\right)=$ ________, where $-\frac{\pi}{2}<x<\frac{\pi}{2}$

$\cos x$

$x$

Complete:
$\arccos\cos x=$ ________.

$\cos x$

$x$

$\sin\sin x$

Complete:
$\arctan\tan x=$ ________.

$\cos x$

$x$

$\sin\sin x$

Is the number sentence true or false?
$\arcsin\left(x\right)=x$ .

True

False

Questions

Time

Score

Understand That Arcsine, Arccosine, And Arctangent Represent The Inverse Of A Sine, Cosine, And Tangent Function Respectively

Is the sentence true or false?In order to have an inverse function for trigonometry, we restrict the domain of each function, so that it is one to one.

True

False

Determine either ﻿f(x)=sin⁡xf\left(x\right)=\sin xf(x)=sinx﻿, then what is the value of ﻿f−1(x)f^{-1}\left(x\right)f−1(x)﻿?

﻿sin⁡x\sin xsinx﻿

﻿arcsin⁡x\arcsin xarcsinx﻿

neither

Determine either ﻿f(x)=xf\left(x\right)=xf(x)=x﻿﻿, then what is the value of ﻿f−1(x)f^{-1}\left(x\right)f−1(x)﻿?

﻿sin⁡x\sin xsinx﻿

﻿arcsin⁡x\arcsin xarcsinx﻿

neither

Is the sentence true or false?﻿arc(arccos⁡cos⁡x)=cos⁡(x)arc\left(\arccos\cos x\right)=\cos\left(x\right)arc(arccoscosx)=cos(x)﻿ is odd function.

True

False

Complete: If ﻿f(x)=tan⁡xf\left(x\right)=\tan xf(x)=tanx﻿, then what is the value of ﻿f−1(x)f^{-1}\left(x\right)f−1(x)﻿?

﻿cos⁡x\cos xcosx﻿

﻿xxx﻿

﻿tan⁡tan⁡x\tan\tan xtantanx﻿

Is the number sentence true or false?﻿sin⁡(0.5)=0.5\sin\left(0.5\right)=0.5sin(0.5)=0.5﻿

True

False

Complete:﻿(sin⁡x)=\left(\sin x\right)=(sinx)=﻿ ________, where ﻿−π2<x<π2-\frac{\pi}{2}<x<\frac{\pi}{2}−2π​<x<2π​﻿

﻿cos⁡x\cos xcosx﻿

﻿xxx﻿

﻿xxx﻿

Complete:﻿arccos⁡cos⁡x=\arccos\cos x=arccoscosx=﻿ ________.

﻿cos⁡x\cos xcosx﻿

﻿xxx﻿

﻿sin⁡sin⁡x\sin\sin xsinsinx﻿

Complete:﻿arctan⁡tan⁡x=\arctan\tan x=arctantanx=﻿ ________.

﻿cos⁡x\cos xcosx﻿

﻿xxx﻿

﻿sin⁡sin⁡x\sin\sin xsinsinx﻿

Is the number sentence true or false?﻿arcsin⁡(x)=x\arcsin\left(x\right)=xarcsin(x)=x﻿.

True

False

Incorrect

Great!

Is the sentence true or false?
In order to have an inverse function for trigonometry, we restrict the domain of each function, so that it is one to one.

Determine either $f\left(x\right)=\sin x$ , then what is the value of $f^{-1}\left(x\right)$ ?

$\sin x$

$\arcsin x$

Determine either $f\left(x\right)=x$ , then what is the value of $f^{-1}\left(x\right)$ ?

$\sin x$

$\arcsin x$

Is the sentence true or false?
$arc\left(\arccos\cos x\right)=\cos\left(x\right)$ is odd function.

Complete: If $f\left(x\right)=\tan x$ , then what is the value of $f^{-1}\left(x\right)$ ?

$\cos x$

$x$

$\tan\tan x$

Is the number sentence true or false?
$\sin\left(0.5\right)=0.5$

Complete:
$\left(\sin x\right)=$ ________, where $-\frac{\pi}{2}<x<\frac{\pi}{2}$

$\cos x$

$x$

$x$

Complete:
$\arccos\cos x=$ ________.

$\cos x$

$x$

$\sin\sin x$

Complete:
$\arctan\tan x=$ ________.

$\cos x$

$x$

$\sin\sin x$

Is the number sentence true or false?
$\arcsin\left(x\right)=x$ .