How do you solve $6 + 2 cos (θ) = 5$ $6+2cos(theta)=5$ ?

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How do you solve $6 + 2 cos (θ) = 5$ $6+2cos(theta)=5$ ?

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Answer 1 · 2015-04-19T18:25:18

$6 + 2 cos x = 5 - \to 2 cos x = - 1 - \to cos x = - \frac{1}{2}$ $6 + 2 cos x = 5 --> 2cos x = -1 --> cos x = -1/2$
Trig table gives answer: $x_{1} = 2 \frac{π}{3} .$ $x_1 = 2pi/3.$
Trig unit circle gives another arc x that has the same cos value:
$x_{2} = 4 \frac{π}{3} .$ $x_2 = 4pi/3.$
Within the interval ( $0, 2 π$ $0, 2pi$ ), there are 2 answers: $2 \frac{π}{3}$ $2pi/3$ and $4 \frac{π}{3}$ $4pi/3$

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How do you solve $6 + 2 cos (θ) = 5$ $6+2cos(theta)=5$ ?

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How do you solve $6 + 2 cos (θ) = 5$ $6+2cos(theta)=5$ ?