What is the value of cos(arctan(6/5)) ?

The value of cos(arctan(6/5)) is (5sqrt(61))/(61)

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cos(arctan(6/5))

cos (arctan (\frac{6}{5}))

\frac{5 61}{61}

Decimal

0.64018 \dots

Solution steps

cos (arctan (\frac{6}{5}))

Rewrite using trig identities:

cos (arctan (\frac{6}{5})) = \frac{1 + ( \frac{6}{5} ) ^{2}}{1 + ( \frac{6}{5} ) ^{2}}

Use the following identity:

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

= \frac{1 + ( \frac{6}{5} ) ^{2}}{1 + ( \frac{6}{5} ) ^{2}}

= \frac{1 + ( \frac{6}{5} ) ^{2}}{1 + ( \frac{6}{5} ) ^{2}}

Simplify

= \frac{5 61}{61}

What is the value of cos(arctan(6/5)) ?
The value of cos(arctan(6/5)) is (5sqrt(61))/(61)