What is the value of cos(arctan(9/40)) ?

The value of cos(arctan(9/40)) is 40/41

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cos(arctan(9/40))

cos (arctan (\frac{9}{40}))

\frac{40}{41}

Decimal Notation

0.97560 \dots

Solution steps

cos (arctan (\frac{9}{40}))

Rewrite using trig identities:

cos (arctan (\frac{9}{40})) = \frac{1 + ( \frac{9}{40} ) ^{2}}{1 + ( \frac{9}{40} ) ^{2}}

Use the following identity:

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

= \frac{1 + ( \frac{9}{40} ) ^{2}}{1 + ( \frac{9}{40} ) ^{2}}

= \frac{1 + ( \frac{9}{40} ) ^{2}}{1 + ( \frac{9}{40} ) ^{2}}

Simplify

= \frac{40}{41}

\frac{31.5}{tan ( 7 5 ^{\circ} )}

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5 (sin (4) + cos (4) + 4 (cos (4) - sin (4)))

arccos (7350)

cos (\frac{12}{15})

What is the value of cos(arctan(9/40)) ?
The value of cos(arctan(9/40)) is 40/41