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11111nata11111 [884]
4 years ago
14

Describe the vector below shown below as an ordered pair. X-value? Y-value?

Mathematics
2 answers:
Cloud [144]4 years ago
6 0
\bf \begin{cases}
x=rcos(\theta )\\
y=rsin(\theta )\\
------\\
r=22\\
\theta =39
\end{cases}\implies (\stackrel{x}{22\cdot cos(39^o)}~,~\stackrel{y}{22\cdot sin(39^o)})
\\\\\\
(x,y)\approx (17.09721115~~,~~13.84504860)
rosijanka [135]4 years ago
3 0
The red vector has a magnitude of 22 and makes an angle of 39 degrees with the horizonal x-axis.

Converting to rectangular form:  x = 22 cos 39 deg and y = 22 sin 39 deg
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Answer:

\displaystyle x=\Big\{\frac{7\pi}{6}+2n\pi, \frac{3\pi}{2}+2n\pi, \frac{11\pi}{6}+2n\pi}\Big\}, n\in\mathbb{Z}

Step-by-step explanation:

We are given the equation:

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First, we can divide everything by 2:

2\sin^2(x)+3\sin(x)+1=0

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\displaystyle \sin(x)=-\frac{1}{2}\text{ or } \sin(x)=-1

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\displaystyle x=\Big\{\frac{7\pi}{6}+2n\pi, \frac{3\pi}{2}+2n\pi, \frac{11\pi}{6}+2n\pi}\Big\}, n\in\mathbb{Z}

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