What is the value of cos(-4/3 pi) ?

The value of cos(-4/3 pi) is -1/2

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cos(-4/3 pi)

cos (- \frac{4}{3} π)

- \frac{1}{2}

Solution steps

cos (- \frac{4}{3} π)

Simplify:

- \frac{4}{3} π = - \frac{4 π}{3}

= cos (- \frac{4 π}{3})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{4 π}{3}) = cos (\frac{4 π}{3})

= cos (\frac{4 π}{3})

Rewrite using trig identities:

cos (π) cos (\frac{π}{3}) - sin (π) sin (\frac{π}{3})

= cos (π) cos (\frac{π}{3}) - sin (π) sin (\frac{π}{3})

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

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

Simplify

= - \frac{1}{2}

25 cos (0)

sec (- 58 5^{\circ})

sin^{3} (9 0^{\circ})

60 cos (4 5^{\circ})

sin^{2} (\frac{5 π}{6}) + cos^{2} (\frac{5 π}{6})