What is rad in degrees?

Question

ScanSolve AI Tutor · Accepted Answer

here are the solutions to the trigonometry questions:

1. What is $\frac{\pi}{3}$ rad in degrees?

To convert radians to degrees, use the conversion factor $\frac{180^\circ}{\pi \text{ rad}}$ .
$\text{Degrees} = \text{Radians} \times \frac{180^\circ}{\pi}$
Substitute the given radian value into the formula.
$\text{Degrees} = \frac{\pi}{3} \times \frac{180^\circ}{\pi}$
Cancel out $\pi$ and perform the multiplication.
$\text{Degrees} = \frac{180^\circ}{3} = 60^\circ$
The correct option is C.
$\boxed{\text{C. } 60^\circ}$
2. Determine the length of an arc which subtends an angle of 0.8 rad at the centre of a circle of radius 10 cm.
The formula for the length of an arc ( $s$ ) is $s = r\theta$ , where $r$ is the radius and $\theta$ is the angle in radians.
Given: $r = 10$ cm, $\theta = 0.8$ rad.
Substitute the given values into the formula.
$s = (10 \text{ cm}) \times (0.8 \text{ rad})$
Calculate the arc length.
$s = 8 \text{ cm}$
The correct option is B.
$\boxed{\text{B. } 8 \text{ cm}}$
3. Calculate the area of a sector containing an angle of 1.5 rad, in a circle of radius 2 cm.
The formula for the area of a sector ( $A$ ) is $A = \frac{1}{2}r^2\theta$ , where $r$ is the radius and $\theta$ is the angle in radians.
Given: $r = 2$ cm, $\theta = 1.5$ rad.
Substitute the given values into the formula.
$A = \frac{1}{2} (2 \text{ cm})^2 (1.5 \text{ rad})$
Calculate the square of the radius.
$A = \frac{1}{2} (4 \text{ cm}^2) (1.5)$
Perform the multiplication.
$A = 2 \text{ cm}^2 \times 1.5$ $A = 3 \text{ cm}^2$
The correct option is A.
$\boxed{\text{A. } 3 \text{ cm}^2}$

Answer