i don't really get what radians are and how to calculate them. i know that the basic pi=180 radians but that's about it. I'm mucking up at becuase i need to know this radian shit for trig/inverse functions. could any of you guyts give me any decent explanations?:mad1:
-
Looking for HSC notes and resources? Check out our Notes & Resources page
radians (1 Viewer)
- Thread starter Mathman26
- Start date
addikaye03
The A-Team
All you gotta know is 180 degree=pi radians and how to convert from degrees to radians and vice versa.
so degrees-->radians : x pi/180
radians --> degrees : x 180/pi
Edited: typo
Last edited:
Tully B.
Green = procrastinating
Isn't it 180 degress = pi radians?
Timothy.Siu
Prophet 9
one revolution is 2pi rads
Dragonmaster262
Unorthodox top student
Solve cosx=1/2 giving your answers in radians.
ninetypercent
ninety ninety ninety
x = pi/3, 5pi/6
basically, you just find the angle in degrees and convert if you're not too comfortable with radians.
basically, you just find the angle in degrees and convert if you're not too comfortable with radians.
Dragonmaster262
Unorthodox top student
I still don't get how you got 5pi/6.
ninetypercent
ninety ninety ninety
ahh sorry. that's a typo. It's supposed to be 5pi/3
philly2000
New Member
- Joined
- Feb 11, 2009
- Messages
- 29
- Gender
- Male
- HSC
- 2010
shoudnt it be 5pi/3 not 5pi/6?
edit: whoops too slow.
edit: whoops too slow.
Dragonmaster262
Unorthodox top student
I still don't get that either.
EDIT: I get it now. My teacher showed me an easier way.
Last edited:
jet
Banned
- Joined
- Jan 4, 2007
- Messages
- 3,148
- Gender
- Male
- HSC
- 2009
Because, for a positive value of cosine, there are two solutions (going by ASTC). So they are theta, and 360 - theta
But we need it in radians, so we do 2π - theta
So, if theta is π/3, then the other angle is 2π - theta = 2π - π/3 = 5π/3
But we need it in radians, so we do 2π - theta
So, if theta is π/3, then the other angle is 2π - theta = 2π - π/3 = 5π/3
Timothy.Siu
Prophet 9
cos x=cos(2pi-x)
gurmies
Drover
technically.
- Joined
- Feb 16, 2005
- Messages
- 8,140
- Gender
- Male
- HSC
- 2006
Radians are the arc length of a unit circle that subtends a certain angle.
So consider the full circumference of a unit circle is 2π units (circumference = 2πr with r = 1). The angle in degrees that a full circle makes is 360 degrees. Therefore, we say that 360 degrees is equivalent to 2π radians.
If we consider an arc of the unit circle that subtends an angle of say 30 degrees at the centre, then the arc length is 30/360 times the full circumference of the unit circle. With the full circumference being 2π, the portion of this that makes up the arc is simply 30/360 x 2π = π/6.
So from this, we can derive some general relationships:
360 degrees ≡ 2π radians
=> 180 degrees = π radians
=> 360 / 2π degrees ≡ 1 radian
So this means:
360x / 2π degrees ≡ x radians
So consider the full circumference of a unit circle is 2π units (circumference = 2πr with r = 1). The angle in degrees that a full circle makes is 360 degrees. Therefore, we say that 360 degrees is equivalent to 2π radians.
If we consider an arc of the unit circle that subtends an angle of say 30 degrees at the centre, then the arc length is 30/360 times the full circumference of the unit circle. With the full circumference being 2π, the portion of this that makes up the arc is simply 30/360 x 2π = π/6.
So from this, we can derive some general relationships:
360 degrees ≡ 2π radians
=> 180 degrees = π radians
=> 360 / 2π degrees ≡ 1 radian
So this means:
360x / 2π degrees ≡ x radians
ForbiddenND
Member
- Joined
- May 29, 2008
- Messages
- 104
- Gender
- Male
- HSC
- 2010
Take a circle with radius 1. Therefore to find out the circumference it is 2(pi)r.
Therefore the circumference = 2(pi). Now take an example, say 30 degrees, thereforce 30degrees/360degrees x 2(pi) = 2(pi)/3 which is how many radians it is. Therefore the general equation is:
1 radian = 180 degrees
I think thats right.....
Therefore the circumference = 2(pi). Now take an example, say 30 degrees, thereforce 30degrees/360degrees x 2(pi) = 2(pi)/3 which is how many radians it is. Therefore the general equation is:
1 radian = 180 degrees
I think thats right.....
Ok to start with if ur gonna use ur calculator to calculate radians u need it to b in the radians function not the degrees (it will hav a R at the top instead of a D)
so pi=180 degrees
to convert from radians to degrees:
and degrees into radians
so that means that:
pi/2 = 180 degrees/2
= 90 degrees
this can be used for other values as well
Copied from my teachers notes, hes a bloody genius.
Geometry uses degrees and minutes to measure angles. Another way to measure angles is in radians. These are useful in circle results and calculus.
One Radian is an angle that an arc of 1 unit substends at the centre of a circle of radius 1 unit.
With Radians, angles can be expressed in terms of pi.
Conversions.
Convert
to degrees.
Convert 50degrees into Radians to 2 d.p.
hopes this helps, seeing as it took close to an hour just to do typing, drawing and that bloody LaTeX program.
Geometry uses degrees and minutes to measure angles. Another way to measure angles is in radians. These are useful in circle results and calculus.
One Radian is an angle that an arc of 1 unit substends at the centre of a circle of radius 1 unit.
With Radians, angles can be expressed in terms of pi.
Conversions.
Convert
Convert 50degrees into Radians to 2 d.p.
hopes this helps, seeing as it took close to an hour just to do typing, drawing and that bloody LaTeX program.