What is the value of cos(arctan(1/2)-3pi) ?

The value of cos(arctan(1/2)-3pi) is -(2sqrt(5))/5

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cos(arctan(1/2)-3pi)

cos (arctan (\frac{1}{2}) - 3 π)

- \frac{2 5}{5}

Solution steps

cos (arctan (\frac{1}{2}) - 3 π)

Rewrite using trig identities:

cos (arctan (\frac{1}{2})) cos (π) + sin (arctan (\frac{1}{2})) sin (π)

= cos (arctan (\frac{1}{2})) cos (π) + sin (arctan (\frac{1}{2})) sin (π)

Rewrite using trig identities:

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

Use the following trivial identity:

cos (π) = (- 1)

Rewrite using trig identities:

sin (arctan (\frac{1}{2})) = \frac{5}{5}

Use the following trivial identity:

sin (π) = 0

= \frac{2 5}{5} (- 1) + \frac{5}{5} \cdot 0

Simplify

= - \frac{2 5}{5}

cos (- 0.01)

tan (\frac{π}{4}) + cot (\frac{π}{4})

12 sin (12 0^{\circ})

6 cos (22 5^{\circ})

arcsin (0.79)

What is the value of cos(arctan(1/2)-3pi) ?
The value of cos(arctan(1/2)-3pi) is -(2sqrt(5))/5