Given that \( \theta \) is an angle in the unit circle such that its terminal side passes through the point (a,b) If the line passing through (a,b) and the origin makes an angle \( \alpha \) with the x-axis, find the values of \( \sin(\alpha) \), \( \cos
Given that \( \theta \) is an angle in the unit circle such that its terminal side passes through the point \((a,b)\):
The coordinates \((a, b)\) on the unit circle imply that \(a = \cos(\theta)\) and \(b = \sin(\theta)\).
Since the line passing through \((a, b)\) and the origin makes an angle \( \alpha \) with the x-axis:
$$ \sin(\alpha) = \frac{b}{\sqrt{a^2 + b^2}} $$
$$ \cos(\alpha) = \frac{a}{\sqrt{a^2 + b^2}} $$
$$ \tan(\alpha) = \frac{b}{a} $$
Given that \( \theta \) is in the second quadrant:
$$ \theta = \pi – \alpha $$