What is the value of cos(arctan(-8)) ?

The value of cos(arctan(-8)) is (sqrt(65))/(65)

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cos(arctan(-8))

cos (arctan (- 8))

\frac{65}{65}

Decimal Notation

0.12403 \dots

Solution steps

cos (arctan (- 8))

Rewrite using trig identities:

cos (arctan (- 8)) = \frac{1 + ( - 8 ) ^{2}}{1 + ( - 8 ) ^{2}}

Use the following identity:

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

= \frac{1 + ( - 8 ) ^{2}}{1 + ( - 8 ) ^{2}}

= \frac{1 + ( - 8 ) ^{2}}{1 + ( - 8 ) ^{2}}

Simplify

= \frac{65}{65}

tan (2 arccos (- \frac{5}{13}))

arctan (\frac{50}{36})

cos (81 0^{\circ})

2 sin (\frac{π}{6}) - 1

arctan (tan (- \frac{3 π}{2}))

What is the value of cos(arctan(-8)) ?
The value of cos(arctan(-8)) is (sqrt(65))/(65)