Question

NEED HELP DUR ON FIRDAY!!!!!!!!!

Fill in the radian measures on the bottom line for 0°, 90°, 180°, 270°, and 360°.

Answer 1

`\begin{array} \cline{1-2}\text{Degrees} & \text{Radians}\\\cline{1-2}0 & 0\\\cline{1-2}90 & \pi/2\\\cline{1-2}180 & \pi\\\cline{1-2}270 & 3\pi/2\\\cline{1-2}360 & 2\pi\\\cline{1-2}\end{array}`

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Step-by-step explanation:

pi radians = 180 degrees by definition

Divide both sides in half

pi/2 radians = 90 degrees

Then multiply both sides by 3

3pi/2 radians = 270 degrees

And finally, we can double both sides of the original equation to get

2pi radians = 360 degrees

As a summary:

• 0 degrees = 0 radians
• 90 degrees = pi/2 radians
• 180 degrees = pi radians
• 270 degrees = 3pi/2 radians
• 360 degrees = 2pi radians

If you are struggling to remember these radian values, then one helpful memorization trick is to convert each fraction to have a denominator of 2.

• 0 = 0pi/2
• pi/2 = 1pi/2
• pi = 2pi/2
• 3pi/2 = 3pi/2
• 2pi = 4pi/2

The numerators of those right-hand-side fractions are: 0pi, 1pi, 2pi, 3pi, and 4pi.

Extra notes:

• You can use word "pi" or the symbol
  `\pi`
• Something like
  `\pi/2` is the same as
  `(\pi)/(2)`
• WolframAlpha is an online tool to help check the answers. A unit circle chart is also a good choice.