What is the supplement of \$pi/4\$ radians in degrees, and what is the complement of 25 degrees in radians?

Supplement of \$\pi/4\$ radians in degrees.

Write down the given angle:

\$\pi/4\$ radians

Use the formula for the supplement:

Supplement = \$180° - (\pi/4 \times (180°)/pi)\$

Substitute the given angle into the formula:

Supplement = 180° - 45°

Simplify to find the supplement:

Supplement = 135°

Complement of 25° in radians:

Write down the given angle:

25°

Use the formula for the Complement:

Complement = \$\pi/2 - (25° \times \pi/(180°))\$

Convert degrees to radians:

\$25° \times (\pi/(180°))\$

Substitute the converted angle into the formula:

Complement = \$(\pi/2 - (5\pi)/36)\$

Simplify to find the complement:

Complement = \$(13\pi)/36\$

So, the supplement of \$pi/4\$ radians in degrees is 135°, and the complement of 25° in radians is \$(13\pi)/36\$ radians.

This option doesn’t match our calculated values. We found the supplement of \$pi/4\$ radians to be 135°, not 45°

45° and \$(pi/36) \$

This option matches the complement of 25° in radians but does not match the supplement of \$pi/4\$ radians in degrees

25° and \$(pi/13)\$

This option doesn’t match our calculated values. We found the supplement of \$pi/4\$ radians to be 135°, not 120°

120° and \$(36pi)/13 \$

This option matches both the supplement of \$pi/4\$ radians in degrees and the complement of 25° in radians

135° and \$(13\pi)/36\$

Option

D

Can you summarize what you’ve understood in the above steps?