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Paraphin [41]
3 years ago
6

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

Mathematics
2 answers:
Svetllana [295]3 years ago
8 0

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

kodGreya [7K]3 years ago
6 0

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)

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