How do you find the values of $θ$ $theta$ given $cos θ = \frac{1}{2}$ $costheta=1/2$ ?

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How do you find the values of $θ$ $theta$ given $cos θ = \frac{1}{2}$ $costheta=1/2$ ?

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Answer 1 · 2016-12-19T05:59:38

$\frac{π}{3}; \frac{5 π}{3}$ $pi/3; (5pi)/3$

Explanation:

$cos θ = \frac{1}{2}$ $cos theta = 1/2$
Trigonometric table of special arcs gives -->
$θ = \frac{π}{3} (or 60^{\circ})$ $theta = pi/3 (or 60^@)$
Unit circle gives another arc $θ$ $theta$ that has the same cos value $(\frac{1}{2})$ $(1/2)$ :
$θ = - \frac{π}{3}$ $theta = - pi/3$ , or $θ = \frac{5 π}{3}$ $theta = (5pi)/3$ (co-terminal).
Answers for $(0, 2 π)$ $(0, 2pi)$
$\frac{π}{3}; \frac{5 π}{3}$ $pi/3; (5pi)/3$

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How do you find the values of $θ$ $theta$ given $cos θ = \frac{1}{2}$ $costheta=1/2$ ?

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How do you find the values of $θ$ $theta$ given $cos θ = \frac{1}{2}$ $costheta=1/2$ ?