Someone please help!

Question

asked Mar 13, 2022 151k views

1 Answer

Mufazzal · Answer 1 · 2022-03-16T23:19:34+0000

Given:

$(\sin x)^2+(\cos x)^2=1$

$\cos \theta = (4√(2))/(7)$

To find:

The value of
$\sin \theta$ .

Solution:

We have,

$\cos \theta = (4√(2))/(7)$

Putting this value in the Pythagorean identity, we get

$(\sin \theta)^2+(\cos \theta)^2=1$

$(\sin \theta)^2+\left((4√(2))/(7)\right)^2=1$

$(\sin \theta)^2+(16(2))/(49)=1$

$(\sin \theta)^2+(32)/(49)=1$

$(\sin \theta)^2=1-(32)/(49)$

$(\sin \theta)^2=(49-32)/(49)$

$(\sin \theta)^2=(17)/(49)$

Taking square root on both sides, we get

$\sin \theta=\pm \sqrt{(17)/(49)}$

$\sin \theta=\pm (√(17))/(7)$

The given value of
$\sin \theta$ is positive. So,
$\sin \theta= (√(17))/(7)$ .

Therefore, the value of value
$\sin \theta$ is
$\sin \theta= (√(17))/(7)$ .