If cot theta= -sqrt{3} text{and} sec theta<0Find sin theta

Find the point on the line $y=5x+3$ that is closet to the origin.

Find an equation of the plane. The plane through the points (2, 1, 2), (3, −8, 6), and (−2, −3, 1)

Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list. Enter the appropriate letter(A,B, C, D or E)in each blank
A . ${\displaystyle \tan \left(\arcsin \left(\frac{x}{8}\right)\right)}$
B . ${\displaystyle \cos \left(ar\sin \left(\frac{x}{8}\right)\right)}$
C. ${\displaystyle \left(\frac{1}{2}\right)\sin \left(2\arcsin \left(\frac{x}{8}\right)\right)}$
D. ${\displaystyle \sin \left(\arctan \left(\frac{x}{8}\right)\right)}$
E. ${\displaystyle \cos \left(\arctan \left(\frac{x}{8}\right)\right)}$

Challenge In $\mathrm{△}ABC,m\mathrm{\angle }B$ is one-third the $m\mathrm{\angle }A\text{and}m\mathrm{\angle }C$ is 37 less than the $m\mathrm{\angle }A.$. What are the measures of the angles of $\mathrm{△}ABC$?

Find the remaining angles for ${\displaystyle △ABC}$. ${\displaystyle m\angle B=30\circ \text{and}m\angle A=\frac{1}{2}m\angle C}$
${\displaystyle m\angle A=\surd \circ }$ and ${\displaystyle m\angle C=\surd \circ }$

Given ${\displaystyle △ABC\cong △DEF}$, name all of the corresponding parts you could prove congruent using CPCTC

Given a right triangle, where one cathetus is ${\displaystyle \bar{A}=11}$ m, the hypothenuse is ${\displaystyle \bar{C}=15}$ m, and ${\displaystyle \mathrm{\angle }c={90}^{\circ }}$ . Find all missing sides ${\displaystyle \left(\bar{B}\right)\text{and}\mathrm{\angle }s\left(\mathrm{\angle }a\text{and}\mathrm{\angle }b\right)}$.