Question

The Pythagorean Identity states that:

(sin x)2 + (cos x)2 = 1
Given cos 6 = 472, find sin .
[?]
sin 0:
O
Simplify the fraction.

Answer 1

`sin(\theta) = (√(17) )/(7)`

Explanation:

We know that:

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

And we know that:

`cos(\theta) = (4√(2))/(7) }`

We want to find the value of the sine function evaluated in theta.

If we replace that in the first equation, we get:

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

`sin(\theta)^2 + ((4*√(2) )/(7)) ^2 = 1`

`sin(\theta)^2 + ((4^2*√(2)^2 )/(7^2)) = 1`

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

Now we can just isolate the sine part of that equation, so we get:

`sin(\theta)^2 = - ((16*2 )/(49)) + 1 = (-32)/(49) + (49)/(49) = (-32 + 49)/(49) = (17)/(49)`

`sin(\theta) = \sqrt{(17)/(49) } = (√(17) )/(√(49) ) = (√(17) )/(7)`

(We can't simplify the fraction anymore)