3 years ago

Find the rectangular coordinates of the point with the polar coordinates ordered pair negative 7 comma 5 pi divided by 3.

1 answer:

6 0

$\bf \begin{array}{clclll}
(-7&,&\frac{5\pi }{3})\\
\uparrow &&\uparrow \\
r&&\theta
\end{array}\qquad 
\begin{array}{clclll}
(x&,&y)\\
\downarrow &&\downarrow \\
r\cdot cos(\theta)&&r\cdot sin(\theta)
\end{array}$

so.. to get the x,y coordinates, or rectangular ones, get the cosine and sine of that angle, and multiply it times the "r"adius

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Find cotθ, cosθ, and secθ, where θ is the angle shown in the figure.

Darina [25.2K]

Answer:

$\cos( \theta) = \frac{5}{8} \\ {8}^{2} = {5}^{2} + {opp}^{2} \\ {opp}^{2} = 64 - 25 = 39 \\ opp = \sqrt{39} \\ \sin(\theta) = \frac{\sqrt{39}}{8} \\ \tan(\theta) = \frac{ \sqrt{39} }{5} \\ \cot(\theta) = \frac{1}{\tan(\theta)} = \frac{1}{\frac{ \sqrt{39} }{5}} \\ \cot(\theta) = \frac{5}{ \sqrt{39} } \\ \csc( \theta) = \frac{1}{\sin(\theta)} = \frac{1}{\frac{\sqrt{39}}{8}} \\ \csc( \theta) = \frac{8}{ \sqrt{39} } \\ \sec( \theta) = \frac{1}{\cos( \theta) } = \frac{1}{ \frac{5}{8} } \\ \sec( \theta) = \frac{8}{5}$