What is the value of cos(arctan(12/5)) ?

The value of cos(arctan(12/5)) is 5/13

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cos(arctan(12/5))

cos (arctan (\frac{12}{5}))

\frac{5}{13}

Decimal Notation

0.38461 \dots

Solution steps

cos (arctan (\frac{12}{5}))

Rewrite using trig identities:

cos (arctan (\frac{12}{5})) = \frac{1 + ( \frac{12}{5} ) ^{2}}{1 + ( \frac{12}{5} ) ^{2}}

Use the following identity:

cos (arctan (x)) = \frac{1 + x ^{2}}{1 + x ^{2}}

= \frac{1 + ( \frac{12}{5} ) ^{2}}{1 + ( \frac{12}{5} ) ^{2}}

= \frac{1 + ( \frac{12}{5} ) ^{2}}{1 + ( \frac{12}{5} ) ^{2}}

Simplify

= \frac{5}{13}

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