Question

PLEASE HELP ME DONT UNDRRSTAND

Answer 1

Answer:

`\sf \sin x = (11√(5))/(33)`

Step-by-step Explanation:

The Pythagorean identity is given by:

`\sf \sin^2 x + \cos^2 x = 1`

Since
`\sf \cos x = (22)/(33)` (and
`\sf x` is in the 1st quadrant, where both sine and cosine are positive), we can use this information to find
`\sf \sin x`.

Let
`\sf \sin x = s`:

`\sf s^2 + \left((22)/(33)\right)^2 = 1`

Now, solve for
`\sf s`:

`\sf s^2 + (484)/(1089) = 1`

Subtract
`\sf (484)/(1089)` from both sides:

`\sf s^2 = (605)/(1089)`

Take the square root of both sides:

`\sf s = \pm \sqrt{(605)/(1089)}`

Since
`\sf x` is in the 1st quadrant, where
`\sf \sin x` is positive, we take the positive square root:

`\sf s = \sqrt{(605)/(1089)}`

Now, simplify if possible:

`\sf s = \sqrt{(605)/(1089)} = (√(605))/(√(1089))`

Since
`\sf √(1089) = 33`:

`\sf s = (√(605))/(33)`

`\sf s = (√(5 * 11^2 ))/(33)`

`\sf s = (11√(5))/(33)`

So,
`\sf \sin x = (11√(5))/(33)`