Question

Given the following use a Pythagorean identity to find sin(0) if 0 is in quadrant II

Answer 1

C.

Explanation:

In trigonometry, we have an equation as following:

`sine^(2) x + cosine^(2) x = 1`

Replace θ into the above equation, we would have:

(sine θ)^2 + (cosine θ)^2 = 1

=> (sine θ)^2 = 1 - (cosine θ)^2 (1)

As given, we have cosine θ = -3/7. Replace it into the equation (1), we have:

(sine θ)^2 = 1 - (-3/7)^2

=>(sine θ)^2 = 1 - 9/49 = 40/49

=> sine θ = ±
`\sqrt{(40)/(49) }` = ±
`(2√(10) )/(7)`

So sine θ =
`(2√(10) )/(7)` or sine θ = -
`(2√(10) )/(7)`

However, as θ is in quadrant II, sine θ has a positive value

=> sine θ =
`(2√(10) )/(7)`

So that the correct answer is C