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

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

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cos(pi+pi/3)

cos (π + \frac{π}{3})

- \frac{1}{2}

Solution steps

cos (π + \frac{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}

arcsin (- 0.625)

csc (\frac{15 π}{8})

2 tan (2 π)

- 10 sin (3 0^{\circ})

2 sin (\frac{7 π}{8})