Question

Simplify sine theta over square root of the quantity 1 minus sine squared theta.

Answer 1

Answer:

tan θ

Step-by-step explanation:

(sin θ) / (√(1 - sin²θ))

$\mathrm{Use\:the\:following\:identity}:\quad \cos ^2\left(x\right)+\sin ^2\left(x\right)=1$

$\mathrm{Therefore\:}1-\sin ^2\left(x\right)=\cos ^2\left(x\right)$

$=\frac{\sin \left(θ\right)}{\sqrt{\cos ^2\left(θ\right)}}$  (The letter i or I is supposed to be theta, the mechanics aren't working)

$\sqrt{\cos ^2\left(θ\right)}=\cos \left(θ\right)$

$=\frac{\sin \left(θ\right)}{\cos \left(θ\right)}$ (sin over cos θ is simply tan θ)

= tan θ

Answer 2

Answer:

a. tan Θ

Step-by-step explanation:

1 - sin²(theta) = cos²(theta)

sqrt[1 - sin²(theta)] = sqrt[cos²(theta)]

= cos(theta)

sin(theta)/cos(theta)

tan(theta)