Question

topic 9: radians and degrees

1. what is the formula to convert from rad to deg?

1. what is the formula to convert from deg to rad?

1. convert the following degree measures to radians:

a. 45^circ
b. 60^circ
c. 225^circ

Explanation:

Identify conversion formulas

To convert between degrees and radians, we use the fundamental relationship that a straight angle is \(180^\circ\) or \(\pi\) radians:

• To convert from radians (RAD) to degrees (DEG), multiply by \(\frac{180^\circ}{\pi}\).
• To convert from degrees (DEG) to radians (RAD), multiply by \(\frac{\pi}{180^\circ}\).

Convert 45 degrees

Using the conversion factor from degrees to radians:

$$ 45^\circ \times \frac{\pi}{180^\circ} = \frac{45\pi}{180} = \frac{\pi}{4} $$

This corresponds to the Special Angles value of \(\frac{\pi}{4}\) radians.

Convert 60 degrees

Using the conversion factor from degrees to radians:

$$ 60^\circ \times \frac{\pi}{180^\circ} = \frac{60\pi}{180} = \frac{\pi}{3} $$

This corresponds to the Special Angles value of \(\frac{\pi}{3}\) radians.

Convert 225 degrees

Using the conversion factor from degrees to radians:

$$ 225^\circ \times \frac{\pi}{180^\circ} = \frac{225\pi}{180} = \frac{5\pi}{4} $$

This corresponds to the Special Angles value of \(\frac{5\pi}{4}\) radians.

Answer:

Question 25

To convert from radians to degrees, multiply the radian measure by \(\frac{180^\circ}{\pi}\):

$$\text{Degrees} = \text{Radians} \times \frac{180^\circ}{\pi}$$

Question 26

To convert from degrees to radians, multiply the degree measure by \(\frac{\pi}{180^\circ}\):

$$\text{Radians} = \text{Degrees} \times \frac{\pi}{180^\circ}$$

Question 27

a. \(45^\circ = \frac{\pi}{4}\) radians

b. \(60^\circ = \frac{\pi}{3}\) radians

c. \(225^\circ = \frac{5\pi}{4}\) radians