What is the value of cos(arctan(-5/12)) ?

The value of cos(arctan(-5/12)) is 12/13

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cos(arctan(-5/12))

cos (arctan (- \frac{5}{12}))

\frac{12}{13}

Decimal Notation

0.92307 \dots

Solution steps

cos (arctan (- \frac{5}{12}))

Rewrite using trig identities:

cos (arctan (- \frac{5}{12})) = \frac{1 + ( - \frac{5}{12} ) ^{2}}{1 + ( - \frac{5}{12} ) ^{2}}

Use the following identity:

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

= \frac{1 + ( - \frac{5}{12} ) ^{2}}{1 + ( - \frac{5}{12} ) ^{2}}

= \frac{1 + ( - \frac{5}{12} ) ^{2}}{1 + ( - \frac{5}{12} ) ^{2}}

Simplify

= \frac{12}{13}

arcsin (\frac{10}{15})

sin (\frac{π}{18}) cos (\frac{7 π}{36}) + cos (\frac{π}{18}) sin (\frac{7 π}{36})

4 \cdot cos (4 5^{\circ})

\frac{tan ( 7 9 ^{\circ} ) - tan ( 1 9 ^{\circ} )}{1 + tan ( 7 9 ^{\circ} ) tan ( 1 9 ^{\circ} )}

csc (5 3^{\circ})

What is the value of cos(arctan(-5/12)) ?
The value of cos(arctan(-5/12)) is 12/13