How do you convert 315 degrees into radians?
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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#.
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
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! :)
