What is the value of cos(arctan(24/7)) ?

The value of cos(arctan(24/7)) is 7/25

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cos(arctan(24/7))

cos (arctan (\frac{24}{7}))

\frac{7}{25}

Decimal Notation

0.28

Solution steps

cos (arctan (\frac{24}{7}))

Rewrite using trig identities:

cos (arctan (\frac{24}{7})) = \frac{1 + ( \frac{24}{7} ) ^{2}}{1 + ( \frac{24}{7} ) ^{2}}

Use the following identity:

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

= \frac{1 + ( \frac{24}{7} ) ^{2}}{1 + ( \frac{24}{7} ) ^{2}}

= \frac{1 + ( \frac{24}{7} ) ^{2}}{1 + ( \frac{24}{7} ) ^{2}}

Simplify

= \frac{7}{25}

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