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The Pythagorean Identity states that:
(sin x)2 + (cos x)2 = 1
Given cos 6 = 472, find sin .
[?]
sin 0:
O
Simplify the fraction.

The Pythagorean Identity States That Sin X2 Cos X2 1 Given Cos 6 472 Find Sin Sin 0 O Simplify The Fraction class=

Sagot :

Answer:

[tex]sin(\theta) = \frac{\sqrt{17} }{7}[/tex]

Step-by-step explanation:

We know that:

sin(x)^2 + cos(x)^2 = 1

And we know that:

[tex]cos(\theta) = \frac{4\sqrt{2}}{7} }[/tex]

We want to find the value of the sine function evaluated in theta.

If we replace that in the first equation, we get:

[tex]sin(\theta)^2 + cos(\theta)^2 = 1[/tex]

[tex]sin(\theta)^2 + (\frac{4*\sqrt{2} }{7}) ^2 = 1[/tex]

[tex]sin(\theta)^2 + (\frac{4^2*\sqrt{2}^2 }{7^2}) = 1[/tex]

[tex]sin(\theta)^2 + (\frac{16*2 }{49}) = 1[/tex]

Now we can just isolate the sine part of that equation, so we get:

[tex]sin(\theta)^2 = - (\frac{16*2 }{49}) + 1 = \frac{-32}{49} + \frac{49}{49} = \frac{-32 + 49}{49} = \frac{17}{49}[/tex]

[tex]sin(\theta) = \sqrt{\frac{17}{49} } = \frac{\sqrt{17} }{\sqrt{49} } = \frac{\sqrt{17} }{7}[/tex]

(We can't simplify the fraction anymore)