Is square root 1 minus cosine squared theta = −sin Θ true? If so, in which quadrants does angle Θ terminate?

Yes it is true because:
(1 - cos^2 x) = sin^2 x Sqr.(1 - cos^2 x) = sin x and (-sinx) True, since sin x negative. Also, x terminates in quadrant 3 and 4. Hope this is helpful

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boffeemadrid boffeemadrid · Answer 2 · 2019-03-27T06:35:59+01:00

Answer:

Step-by-step explanation:

The given equation is:

[tex]\sqrt{1-cos^2{\theta}}=-sin{\theta}[/tex]

Taking the Left hand side of the above equation, we get

=[tex]\sqrt{1-cos^2{\theta}}[/tex]

=[tex]\sqrt{sin^2{\theta}}[/tex] (Because [tex]sin^2{\theta}+cos^2{\theta}=1[/tex])

=[tex]{\pm}sin{\theta}[/tex]

Thus, [tex]\sqrt{1-cos^2{\theta}}=-sin{\theta}[/tex] is true.

Now, since [tex]sin{\theta}[/tex] is negative, therefore it terminates in the third and the fourth quadrant because in third and fourth quadrant,[tex]sin{\theta}[/tex] is negative.