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Evaluate cos 4π/3?

1 Answer

Apr 26, 2018

$- \frac{1}{2}$ $-1/2$

Explanation:

$cos (\frac{4 π}{3}) = cos (π + \frac{π}{3})$ $cos((4pi)/3)=cos(pi+pi/3)$

$= - cos (\frac{π}{3})$ $=-cos(pi/3)$ $\to Using Quadrant sign for cosine function$ $color(green)(rarr"Using Quadrant sign for cosine function"$

$= - \frac{1}{2}$ $=-1/2$

Or you could do it with the Sum and Difference Identities

$cos (π + \frac{π}{3}) = cos π \cdot cos (\frac{π}{3}) - sin π \cdot sin (\frac{π}{3})$ $cos(pi+pi/3)=cospi*cos(pi/3)-sinpi*sin(pi/3)$

$= (- 1) (\frac{1}{2}) - (0) (\frac{\sqrt{3}}{2}) = - \frac{1}{2}$ $=(-1)(1/2)-(0)(sqrt3/2)=-1/2$

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