Question

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

Answer 1

Answer:

$(\sqrt{q^2-p^2} + p) / q$

Step-by-step explanation:

sinΘ = p/q

cosΘ=$\sqrt{1-sin^2\theta}$ = $\sqrt{1-(p/q)^2}$ = $\sqrt{q^2-p^2} / q$

cosΘ+sinΘ =  $\sqrt{q^2-p^2} / q$ + p/q = $(\sqrt{q^2-p^2} + p) / q$