How do you convert 315 degrees into radians?

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25
Jul 11, 2015

Answer:

#7/4 pi# radians

Explanation:

To change from degrees to radians use the following formula:

degrees#*(pi# radians#/180# degrees#)#

the #(pi/180)# means that for every #pi# radians you go around the unit circle, you've gone #180# degrees.

So, taking our #315# degrees and plugging into our equation we get:

#315# degrees#*(pi# radians#/180# degrees#)#

The "degrees" cancel out, then we are left with:

#315/180*pi# radians

#315# and #180# are both divisible by #45#, so

#315/180=7/4#

So, then we just need to multiply by #pi# radians and we get:

#7/4*pi# radians = #7/4 pi# radians

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6
Apr 18, 2015

With this proportion:

#alpha_d:alpha_r=180°:pi#

in whitch #alpha_d# is the measure of the angle in degree,

and #alpha_r# is the measure of the angle in radians.

So, if you want to convert an angle from radians in degree:

#a_d=(alpha_r*180°)/pi#

andif you want to convert an angle from degree to radians:

#a_r=(alpha_d*pi)/(180°)#.

In our case:

#a_r=(315°*pi)/(180°)=7/4pi#.

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4
Mar 11, 2017

Answer:

#7/4 pi# #"radians"#

Explanation:

The formula for converting degrees to radians is

#color(brown)("radians"="degrees"*pi/180#

#rarr"radians"=(315*pi)/(180)#

#rarr"radians"=(cancel315^7*pi)/cancel(180)^4#

#color(green)(rArr7/4pi# #color(green)("radians"#

Hope this helps! :)

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