How do you solve $sin(x + pi) = 0.5$ between $0 < x < 2pi$ ?

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Answer 1 · 2015-07-22T17:07:01

Solve sin (x + pi) = 0.5

Ans: $(7pi)/6 and (11pi)/6$

Trig table --> $sin (x + pi) = 0.5 = sin ((pi)/6)$
Trig unit circle gives another arc $(x + pi) = (pi - pi/6) = -pi/6$

a. $x + pi = pi/6 -> x = pi/6 - pi = (-5pi)/6$

b. $x + pi = pi - pi/6 = - pi/6$

On the trig circle, arc $(-5pi)/6$ is the arc $(7pi)/6$ and the arc $(-pi/6)$ is the arc $((11p)/6)$
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How do you solve sin(x + pi) = 0.5sin(x + pi) = 0.5 between 0 < x < 2pi0 < x < 2pi?