What is the value of cos(pi-arctan(1/3)) ?

The value of cos(pi-arctan(1/3)) is -(3sqrt(10))/(10)

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cos(pi-arctan(1/3))

cos (π - arctan (\frac{1}{3}))

- \frac{3 10}{10}

Solution steps

cos (π - arctan (\frac{1}{3}))

Rewrite using trig identities:

cos (π) cos (arctan (\frac{1}{3})) + sin (π) sin (arctan (\frac{1}{3}))

= cos (π) cos (arctan (\frac{1}{3})) + sin (π) sin (arctan (\frac{1}{3}))

Use the following trivial identity:

cos (π) = (- 1)

Rewrite using trig identities:

cos (arctan (\frac{1}{3})) = \frac{3 10}{10}

Use the following trivial identity:

sin (π) = 0

Rewrite using trig identities:

sin (arctan (\frac{1}{3})) = \frac{10}{10}

= (- 1) \frac{3 10}{10} + 0 \cdot \frac{10}{10}

Simplify

= - \frac{3 10}{10}

arccos (\frac{3}{29})

\frac{18}{sin ( 3 2 ^{\circ} )}

\frac{sin ( \frac{π}{2} )}{π}

tan (- \frac{2 π}{7})

cos (\frac{7}{4})

What is the value of cos(pi-arctan(1/3)) ?
The value of cos(pi-arctan(1/3)) is -(3sqrt(10))/(10)