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The Pythagorean Identity states that: (sin x)^2 + (cos x)^2 = 1

Given cos 0 = 5/3, find sin 0

sin 0 = ?/?

Simplify the fraction.

The Pythagorean Identity States That Sin X2 Cos X2 1 Given Cos 0 53 Find Sin 0 Sin 0 Simplify The Fraction class=

Sagot :

AǫᴜᴀWɪᴢ

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:sin(\theta) = \cfrac{2}{3} [/tex]

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[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: \cos {}^{2} ( \theta) + \sin {}^{2} ( \theta) = 1[/tex]

[tex]\qquad \tt \rightarrow \: {\bigg( \cfrac{ \sqrt{5}}{3} \bigg) }^{2} + \sin {}^{2} ( \theta) = 1[/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{5}{9} + \sin {}^{2} ( \theta) = 1[/tex]

[tex]\qquad \tt \rightarrow \: \sin {}^{2} ( \theta) = 1 - \cfrac{5}{9} [/tex]

[tex]\qquad \tt \rightarrow \: \sin {}^{2} ( \theta) = \cfrac{9 - 5}{9} [/tex]

[tex]\qquad \tt \rightarrow \: \sin {}^{2} ( \theta) = \cfrac{4}{9} [/tex]

[tex]\qquad \tt \rightarrow \: \sin {}^{} ( \theta) = \sqrt \cfrac{4}{9} [/tex]

[tex]\qquad \tt \rightarrow \: \sin {}^{} ( \theta) = \pm \cfrac{2}{3} [/tex]

Generally, only positive value is taken :

[tex]\qquad \tt \rightarrow \: \sin {}^{} ( \theta) = \cfrac{2}{3} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

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