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

The value of -3+4cos((4pi)/3) is -5

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-3+4cos((4pi)/3)

- 3 + 4 cos (\frac{4 π}{3})

- 5

Solution steps

- 3 + 4 cos (\frac{4 π}{3})

Rewrite using trig identities:

cos (\frac{4 π}{3}) = cos^{2} (\frac{2 π}{3}) - sin^{2} (\frac{2 π}{3})

= - 3 + 4 (cos^{2} (\frac{2 π}{3}) - sin^{2} (\frac{2 π}{3}))

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

= - 3 + 4 (- \frac{1}{2})^{2} - (\frac{3}{2})^{2}

Simplify

- 3 + 4 (- \frac{1}{2})^{2} - (\frac{3}{2})^{2} : - 5

= - 5

sin (\frac{35 π}{6})

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cos (6 \cdot π)