What is the value of cos(690) ?

The value of cos(690) is (sqrt(3))/2

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cos(690)

cos (69 0^{\circ})

\frac{3}{2}

Solution steps

cos (69 0^{\circ})

cos (69 0^{\circ}) = cos (33 0^{\circ})

= cos (33 0^{\circ})

Rewrite using trig identities:

cos (18 0^{\circ}) cos (15 0^{\circ}) - sin (18 0^{\circ}) sin (15 0^{\circ})

= cos (18 0^{\circ}) cos (15 0^{\circ}) - sin (18 0^{\circ}) sin (15 0^{\circ})

Use the following trivial identity:

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

Use the following trivial identity:

cos (15 0^{\circ}) = - \frac{3}{2}

Use the following trivial identity:

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

Use the following trivial identity:

sin (15 0^{\circ}) = \frac{1}{2}

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

Simplify

= \frac{3}{2}

2 cos^{2} (\frac{π}{12}) - 1

csc (3 π)

\frac{1}{2} sin (π)

cot (- \frac{7 π}{6})

sin (8 8^{\circ})