What is the value of cos(arctan(5/4)) ?

The value of cos(arctan(5/4)) is (4sqrt(41))/(41)

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cos(arctan(5/4))

cos (arctan (\frac{5}{4}))

\frac{4 41}{41}

Decimal Notation

0.62469 \dots

Solution steps

cos (arctan (\frac{5}{4}))

Rewrite using trig identities:

cos (arctan (\frac{5}{4})) = \frac{1 + ( \frac{5}{4} ) ^{2}}{1 + ( \frac{5}{4} ) ^{2}}

Use the following identity:

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

= \frac{1 + ( \frac{5}{4} ) ^{2}}{1 + ( \frac{5}{4} ) ^{2}}

= \frac{1 + ( \frac{5}{4} ) ^{2}}{1 + ( \frac{5}{4} ) ^{2}}

Simplify

= \frac{4 41}{41}

csc (- 39 0^{\circ})

2 (cos (9 0^{\circ}) + i sin (9 0^{\circ}))

sin (0.4 \cdot 4 \cdot π)

\frac{125}{tan ( 7 )}

7 cos (\frac{3 π}{4}) - 7 cos (\frac{π}{4})

What is the value of cos(arctan(5/4)) ?
The value of cos(arctan(5/4)) is (4sqrt(41))/(41)