1. ## Trigonometry Help [Q1]

Question:
Given $x = \arcsin \frac{1}{3}$ , find the exact value of:
a. $\cos x$
b. $\tan x$
c. $\cot x$
d. $\sec x$
e. $\csc x$

Attempt:

a. $\cos x$

$= \cos (x = \arcsin \frac{1}{3})$

$= 0.942809041$

$\color{red}{= 2 \frac{\sqrt{2}}{3}}$

How can I get the fraction answer?

2. Originally Posted by looi76
Question:
Given $x = \arcsin \frac{1}{3}$ , find the exact value of:
a. $\cos x$
b. $\tan x$
c. $\cot x$
d. $\sec x$
e. $\csc x$

Attempt:

a. $\cos x$

$= \cos (x = \arcsin \frac{1}{3})$

$= 0.942809041$

$\color{red}{= 2 \frac{\sqrt{2}}{3}}$

How can I get the fraction answer?
$x= \sin^{-1}\left(\frac{1}{3}\right)$

$\Rightarrow \sin x =\frac{1}{3}$

$\cos x = \sqrt{1-\sin^2 x}=\sqrt{1-\left(\frac{1}{3}\right)^2 }=\sqrt{\frac{8}{9}}=\frac{2\sqrt{2}}{3}$

$\tan x = \frac{\sin x}{\cos x}=\frac{.......}{.......}$ finish it.

$\cot x = \frac{1}{\tan x}=\frac{1}{.......}$ finish it.

$\sec x = \frac{1}{\cos x}=\frac{1}{.......}$ finish it.

$\csc x = \frac{1}{\sin x}=\frac{1}{.......}$ finish it.

got it ???

3. Originally Posted by Shyam
$x= \sin^{-1}\left(\frac{1}{3}\right)$

$\Rightarrow \sin x =\frac{1}{3}$

$\cos x = \sqrt{1-\sin^2 x}=\sqrt{1-\left(\frac{1}{3}\right)^2 }=\sqrt{\frac{8}{9}}=\frac{2\sqrt{2}}{3}$

$\tan x = \frac{\sin x}{\cos x}=\frac{.......}{.......}$ finish it.

$\cot x = \frac{1}{\tan x}=\frac{1}{.......}$ finish it.

$\sec x = \frac{1}{\cos x}=\frac{1}{.......}$ finish it.

$\csc x = \frac{1}{\sin x}=\frac{1}{.......}$ finish it.

got it ???
$\cos x = \pm \sqrt{1-\sin^2 x}=\pm \sqrt{1-\left(\frac{1}{3}\right)^2 }=\pm \sqrt{\frac{8}{9}}=\pm \frac{2\sqrt{2}}{3}$

CB