What is the value of cos(arctan(5/2)) ?

The value of cos(arctan(5/2)) is (2sqrt(29))/(29)

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cos(arctan(5/2))

cos (arctan (\frac{5}{2}))

\frac{2 29}{29}

Decimal Notation

0.37139 \dots

Solution steps

cos (arctan (\frac{5}{2}))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{2 29}{29}

csc (\frac{23 π}{4})

2 + 2 sin (\frac{π}{6})

- cot (\frac{π}{4}) + csc (\frac{π}{4})

arcsin (\frac{0}{5})

arcsin (0.385)

What is the value of cos(arctan(5/2)) ?
The value of cos(arctan(5/2)) is (2sqrt(29))/(29)