Question

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.

Answer 1

`\quad \huge \quad \quad \boxed{ \tt \:Answer }`

`\qquad \tt \rightarrow \:sin(\theta) = \cfrac{2}{3}`

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`\large \tt Solution \: :`

`\qquad \tt \rightarrow \: \cos {}^(2) ( \theta) + \sin {}^(2) ( \theta) = 1`

`\qquad \tt \rightarrow \: {\bigg( \cfrac{ √(5)}{3} \bigg) }^(2) + \sin {}^(2) ( \theta) = 1`

`\qquad \tt \rightarrow \: \cfrac{5}{9} + \sin {}^(2) ( \theta) = 1`

`\qquad \tt \rightarrow \: \sin {}^(2) ( \theta) = 1 - \cfrac{5}{9}`

`\qquad \tt \rightarrow \: \sin {}^(2) ( \theta) = \cfrac{9 - 5}{9}`

`\qquad \tt \rightarrow \: \sin {}^(2) ( \theta) = \cfrac{4}{9}`

`\qquad \tt \rightarrow \: \sin {}^{} ( \theta) = \sqrt \cfrac{4}{9}`

`\qquad \tt \rightarrow \: \sin {}^{} ( \theta) = \pm \cfrac{2}{3}`

Generally, only positive value is taken :

`\qquad \tt \rightarrow \: \sin {}^{} ( \theta) = \cfrac{2}{3}`

Answered by : ❝ AǫᴜᴀWɪᴢ ❞