Solve the problem for the given information.
-Find the equation of a line passing through the origin so that the sine of the angle between the line in quadrant $\mathrm { I }$ and the positive $\mathrm { x }$-axis is $\frac { \sqrt { 3 } } { 2 }$.
A) $y = \frac { \sqrt { 3 } } { 3 } x$
B) $y = \sqrt { 3 } x$
C) $y = \frac { \sqrt { 3 } } { 2 } x$
D) $y = x$

Question

Quizplus · Accepted Answer

The sine of the angle between the line and the positive x-axis is equal to the slope of the line when the line passes through the origin. Since the sine of the angle is given as $\frac{\sqrt{3}}{2}$, and the slope of a line is the tangent of the angle it makes with the positive x-axis, we look for a slope that corresponds to an angle whose sine is $\frac{\sqrt{3}}{2}$. The angle whose sine is $\frac{\sqrt{3}}{2}$ is $60^\circ$, and the tangent of $60^\circ$ (which is the slope of the line) is $\sqrt{3}$. Therefore, the equation of the line is $y = \sqrt{3}x$.

Solve the Problem for the Given Information I\mathrm { I }I

Solve the Problem for the Given Information $\mathrm { I }$