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polet [3.4K]
4 years ago
6

Find the exact value of cos (arcsin (five divided by thirteen)). thirteen over twelve three times the square root of thirteen di

vided by thirteen twelve over thirteen two times the square root of thirteen divided by thirteen
Mathematics
1 answer:
irakobra [83]4 years ago
7 0

Answer:

\frac{12}{13}

Step-by-step explanation:

We are asked to find the exact value of \cos(\arcsin \frac{5}{13}).

Firstly, let's call y = \arcsin \frac{5}{13} ⇒ \sin y=\frac{5}{13}.

Since \cos(\arcsin \frac{5}{13})=\cos y

\cos(\arcsin \frac{5}{13}) = \sqrt{1-\sin^2y}=\sqrt{1-(\frac{5}{13})^2}=\sqrt{1-\frac{25}{169}}=\sqrt{\frac{144}{169}}=\frac{12}{13}

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