How do you find the values of $θ$ $theta$ given $cos θ = \frac{\sqrt{2}}{2}$ $costheta=sqrt2/2$ ?

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How do you find the values of $θ$ $theta$ given $cos θ = \frac{\sqrt{2}}{2}$ $costheta=sqrt2/2$ ?

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Answer 1 · 2018-02-12T01:53:34

$t = \frac{π}{4} + 2 k π$ $t = pi/4 + 2kpi$
$t = \frac{7 π}{4} + 2 k π$ $t = (7pi)/4 + 2kpi$

Explanation:

$cos t = \frac{\sqrt{2}}{2}$ $cos t = sqrt2/2$
Trig table and unit circle give 2 solutions -->
$t = \pm \frac{π}{4}$ $t = +- pi/4$
Note that $t = \frac{7 π}{4}$ $t = (7pi)/4$ is co-terminal to $t = (- \frac{π}{4})$ $t = (-pi/4)$ .
Therefor the 2 answers are:
$t = \frac{π}{4} + 2 k π$ $t = pi/4 + 2kpi$ , and
$t = \frac{7 π}{4} + 2 k π$ $t = (7pi)/4 + 2kpi$

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How do you find the values of $θ$ $theta$ given $cos θ = \frac{\sqrt{2}}{2}$ $costheta=sqrt2/2$ ?

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How do you find the values of $θ$ $theta$ given $cos θ = \frac{\sqrt{2}}{2}$ $costheta=sqrt2/2$ ?