Question

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

cos(0) = -1/5

Answer 1

`\sin(\theta) = (2√(6))/(5)`

Explanation:

`\theta \in [(\pi)/(2); \pi]\\cos(\theta) = (-1)/(5)`

By the Fundamental Theorem of Trigonometry =>
`\sin(\theta) = \pm √((1-\cos^2(\theta)))`

The positive version for
`\theta \in [0, \pi]`. And the negative for
`\theta \in (\pi; 2\pi)`

Meaning sin is positive in the problem =>
`\sin(\theta) = √(1 - \cos^2(\theta)) = \sqrt{1-(1)/(25)} = \sqrt{(24)/(25)} = (2√(6))/(5)`