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

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

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Answer 1 · 2015-07-22T17:07:01

Solve sin (x + pi) = 0.5

Ans: $\frac{7 π}{6} and \frac{11 π}{6}$ $(7pi)/6 and (11pi)/6$

Explanation:

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

a. $x + π = \frac{π}{6} \to x = \frac{π}{6} - π = \frac{- 5 π}{6}$ $x + pi = pi/6 -> x = pi/6 - pi = (-5pi)/6$

b. $x + π = π - \frac{π}{6} = - \frac{π}{6}$ $x + pi = pi - pi/6 = - pi/6$

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

1 Answer

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How do you solve sin(x + pi) = 0.5sin(x+π)=0.5sin(x + pi) = 0.5 between 0 < x < 2pi0<x<2π0 < x < 2pi?

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