Question

Use the Pythagorean identity

to find sin x.
COS X =
sin x =
8
17
?
Enter

Answer 1

`(15)/(17)`

Explanation:

`{ \sin(x) }^(2) + { \cos(x) }^(2) = 1`

`\cos(x) = 8 / 17`

`\sin(x) = \sqrt{1 - { \cos(x) }^(2) }`

`\sin(x) = \sqrt{1 - {(8 / 17)}^(2) }`

`\sin(x) = 15 / 17`

Answer 2

`sin\ x = (15)/(17)`

Explanation:

So in this case, it's similar to the previous question you asked, except this time you know cosine, and as you may know cosine is defined as:
`(adjacent)/(hypotenuse)` and sine is defined as:
`(opposite)/(hypotenuse)`. So all we need to solve for is the opposite side, but since we know two sides, we can solve for the other using the Pythagorean identity:
`a^2+b^2=c^2`

Plug in known values:

`8^2 + b^2 = 17^2`

Simplify:

`64 + b^2 = 289\\b^2 = 225\\b = 15`

So the opposite side is 15, and the hypotenuse is already given, in this case it's 17 (the denominator of cosine). So plugging this into the definition of sin gives you:
`(15)/(17)`