Problem 19 - Precalculus Essentials

Question

Convert each angle in degrees to radians. Express your answer as a multiple of \(\pi\). $$-225^{\circ}$$

Step-by-Step Solution

Answer

The angle \(-225^{\circ}\) in radians is \(-5/4\(\pi\)\)

Step 1: Express the given angle in terms of \(\pi\)

Write the given angle as a fraction with 180 in the denominator to express it in terms of \(\pi\). So, \(-225^{\circ}\) is expressed as \(-225/\(180\)\).

Step 2: Simplify the fraction

Next, simplify the fraction \(-225/180\) to find its simplest form. The greatest common divisor (gcd) of 225 and 180 is 45. So, both the numerator and denominator should be divided by the gcd. When we perform this operation, we have \(-225/180 = -5/4\).

Step 3: Replace the denominator with \(\pi\)

Finally, replace the denominator (which is 180 degrees), with \(\pi\) radians to get \(-5/4\(\pi\)\) radians.