What is the value of cos(1035) ?

The value of cos(1035) is (sqrt(2))/2

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cos(1035)

cos (103 5^{\circ})

\frac{2}{2}

Solution steps

cos (103 5^{\circ})

cos (103 5^{\circ}) = cos (31 5^{\circ})

= cos (31 5^{\circ})

Rewrite using trig identities:

cos (18 0^{\circ}) cos (13 5^{\circ}) - sin (18 0^{\circ}) sin (13 5^{\circ})

= cos (18 0^{\circ}) cos (13 5^{\circ}) - sin (18 0^{\circ}) sin (13 5^{\circ})

Use the following trivial identity:

cos (18 0^{\circ}) = (- 1)

Use the following trivial identity:

cos (13 5^{\circ}) = - \frac{2}{2}

Use the following trivial identity:

sin (18 0^{\circ}) = 0

Use the following trivial identity:

sin (13 5^{\circ}) = \frac{2}{2}

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

Simplify

= \frac{2}{2}

arctan (\frac{1}{- 4})

18 \cdot cos (3 2^{\circ})

- sec (π)

sec (78 0^{\circ})

\frac{cot ( 0 )}{csc ( 0 )}