Question

convert \\(\frac{5\pi}{4}\\) radians to degrees.

Explanation:

Identify the given angle in radians

The problem asks to convert the angle from radians to degrees.
The given angle is:

$$ \theta = \frac{5\pi}{4} \text{ radians} $$

State the conversion factor

To convert from radians to degrees, we use the relationship:

$$ 180^\circ = \pi \text{ radians} $$

Therefore, the conversion factor is:

$$ \frac{180^\circ}{\pi} $$

Calculate the angle in degrees

Multiply the given radian measure by the conversion factor:

$$ \theta_{\text{degrees}} = \frac{5\pi}{4} \times \frac{180^\circ}{\pi} $$

Simplify the expression

Cancel out the common factor \(\pi\):

$$ \theta_{\text{degrees}} = \frac{5}{4} \times 180^\circ $$

Divide \(180\) by \(4\):

$$ 180 \div 4 = 45 $$

Multiply \(5\) by \(45\):

$$ 5 \times 45^\circ = 225^\circ $$

Answer:

Convert <blank>\(\frac{5\pi}{4}\)</blank> radians to degrees.
The answer is <blank>\(225^\circ\)</blank>.