Question

(a) the radian measure of an angle θ is the length of the select that subtends the angle in a circle of radius select. (b) to convert degrees to radians, we multiply by . (c) to convert radians to degrees, we multiply by . (d) what does it mean for an angle to be in standard position? o an angle is in standard position if it is drawn in the xy - plane with its vertex on the positive x - axis and its initial side at the origin. o an angle is in standard position if it is drawn in the xy - plane with its vertex at the origin and its initial side on the positive y - axis. o an angle is in standard position if it is drawn in the xy - plane with its vertex at the origin and its initial side on the negative x - axis. o an angle is in standard position if it is drawn in the xy - plane with its vertex at the origin and its initial side on the positive x - axis. sketch the following angles in standard position: 2π/3, -π/4, 400°, 210°.

Explanation:

Step1: Recall degree - radian conversion formula

The conversion formula from degrees to radians is $\text{Radians}=\text{Degrees}\times\frac{\pi}{180^{\circ}}$, and from radians to degrees is $\text{Degrees}=\text{Radians}\times\frac{180^{\circ}}{\pi}$.

Step2: Answer part (a)

The radian measure of an angle $\theta$ is the length of the arc that subtends the angle in a circle of radius $1$.

Step3: Answer part (b)

To convert degrees to radians, we multiply by $\frac{\pi}{180^{\circ}}$.

Step4: Answer part (c)

To convert radians to degrees, we multiply by $\frac{180^{\circ}}{\pi}$.

Step5: Answer part (d)

An angle is in standard position if it is drawn in the $xy -$plane with its vertex at the origin and its initial side on the positive $x -$axis.

Answer:

(a) the length of the arc that subtends the angle in a circle of radius 1
(b) $\frac{\pi}{180^{\circ}}$
(c) $\frac{180^{\circ}}{\pi}$
(d) An angle is in standard position if it is drawn in the $xy -$plane with its vertex at the origin and its initial side on the positive $x -$axis.