Question

If sin Ѳ = p/q, find the value of cos Ѳ + sin Ѳ in terms of p and q

Answer 1

Step-by-step explanation:

$\sin(Ѳ) = \frac{opp}{hyp} = \frac{p}{q}$

In a right angle triangle,

hypotenuse = p

opposite side = q

According to Pythagoras Theorem,

adj² + opp² = hyp²

adj² = hyp² - opp²

adj² = q² - p²

$adj = \sqrt{ {q}^{2} - {p}^{2} }$

$\cos(Ѳ) = \frac{adj}{hyp} = \frac{ \sqrt{ {q}^{2} - {p}^{2} } }{q}$

$\sin(Ѳ) + \cos(Ѳ) = \frac{p}{q} + \frac{ \sqrt{ {p}^{2} + {q}^{2} } }{q}$

$= \frac{p + \sqrt{ {p}^{2} + {q}^{2} } }{q}$