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zavuch27 [327]
2 years ago
10

What are the solutions to the equation Sine (x + StartFraction 7 pi Over 2 EndFraction) = negative StartFraction StartRoot 3 End

Root Over 2 EndFraction over the interval [0, 2Pi]?
Mathematics
2 answers:
Blababa [14]2 years ago
5 0

Answer:

C. π/6 & 11π/6

Step-by-step explanation:

If you graph the equation ( Sin (x+7π/2)=-√3/2) and look between 0 & 2π, you'll see that the lines intersect the x-axis at π/6 & 11π/6.

il63 [147K]2 years ago
4 0

Given:

The equation is

\sin\left(x+\dfrac{7\pi}{2}\right)=-\dfrac{\sqrt{3}}{2}

To find:

The solutions of given equation over the interval [0,2\pi].

Solution:

We have,

The equation is

\sin\left(x+\dfrac{7\pi}{2}\right)=-\dfrac{\sqrt{3}}{2}

\sin\left(x+\dfrac{7\pi}{2}\right)=-\sin \dfrac{\pi }{3}

\sin\left(x+\dfrac{7\pi}{2}\right)=\sin (-\dfrac{\pi }{3})

If \sin x=\sin y, then x=n\pi +(-1)^ny.

Over the interval [0,2\pi].

x+\dfrac{7\pi}{2}=4\pi-\dfrac{\pi }{3} and x+\dfrac{7\pi}{2}=5\pi+\dfrac{\pi }{3}

x=\dfrac{11\pi }{3}-\dfrac{7\pi}{2} and x=\dfrac{16\pi}{3}-\dfrac{7\pi}{2}

x=\dfrac{22\pi-21\pi }{6} and x=\dfrac{32\pi-21\pi }{6}

x=\dfrac{\pi}{6} and x=\dfrac{11\pi }{6}

Therefore, the two solutions are tex]x=\dfrac{\pi}{6}[/tex] and x=\dfrac{11\pi }{6}.

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