What is the value of cos(1380) ?

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cos(1380)

cos (138 0^{\circ})

\frac{1}{2}

Solution steps

cos (138 0^{\circ})

cos (138 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 (- \frac{3}{3})

\frac{1}{cos ^{2} ( 4 5 ^{\circ} )}

4 cos (29 0^{\circ})

2 cos (4 0^{\circ})

arccos (0.73)