What is the value of cos(1020) ?

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cos(1020)

cos (102 0^{\circ})

\frac{1}{2}

Solution steps

cos (102 0^{\circ})

cos (102 0^{\circ}) = cos (30 0^{\circ})

= cos (30 0^{\circ})

Rewrite using trig identities:

cos (18 0^{\circ}) cos (12 0^{\circ}) - sin (18 0^{\circ}) sin (12 0^{\circ})

= cos (18 0^{\circ}) cos (12 0^{\circ}) - sin (18 0^{\circ}) sin (12 0^{\circ})

Use the following trivial identity:

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

Use the following trivial identity:

cos (12 0^{\circ}) = - \frac{1}{2}

Use the following trivial identity:

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

Use the following trivial identity:

sin (12 0^{\circ}) = \frac{3}{2}

= (- 1) (- \frac{1}{2}) - 0 \cdot \frac{3}{2}

Simplify

= \frac{1}{2}

arctan (tan (- \frac{4 π}{9}))

100 cos (7 0^{\circ})

\frac{sin ( 4 0 ^{\circ} ) - sin ( 2 0 ^{\circ} )}{cos ( 4 0 ^{\circ} ) - cos ( 2 0 ^{\circ} )}

cos (\frac{π}{6}) cos (\frac{π}{6}) - sin (\frac{π}{6}) sin (\frac{π}{6})

\frac{24 sin ( 2 2 ^{\circ} )}{sin ( 4 0 ^{\circ} )}