0
What is the relationship between the arc length and the radius of a circle when the central angle is defined in radians?
Wiki User
∙ 7y agoWant this question answered?
Be notified when an answer is posted
Add your answer:
Earn +20 pts
Application of relation between arc of length and central angle?
The relation between the arc of length and the central angle is that the arc of length divided by one of the sides is the central angle in radians. If the arc is a full circle, then the central angle is 2pi radians or 360 degrees.
What is the measure of the central angle of a circle with the arc length of 29.21 and the circumference of 40.44?
arc length/circumference = central angle/2*pi (radians) So, central angle = 2*pi*arc length/circumference = 4.54 radians. Or, since 2*pi radians = 360 degrees, central angle = 360*arc length/circumference = 260.0 degrees, approx.
Is tangent ever undefined?
Yes. the tangents of odd multiples of pi/2 radians are not defined.
Deg per sec to rad per sec?
If you are asking for the conversion formulas, then think of the relationship between degress and radians. 360 degress = 2*pi radians, thus to convert every degree to radians, we divide both sides of the equation by 360. 1 degree = 2*pi/360 radians = pi/180 radians. thus to convert degrees into radians, just multiply the number of degrees to pi/180, where pi = 3.141592... by the way, the per sec appended on the unit does not matter in the conversion since both units are in per sec anyway
What is Relation between the length of the circular arc and the radian measures of its central angle?
You can think of an arc as a fraction of the circumferance of a circle. Also, a complete circle is 2pi radians, so any central angle is THETA / 2pi of a complete circle. Multiply by the circumferance to get the length of the arc: THETA / 2pi * 2(pi)(r) = THETA * r or the length of the arc is simply the radius times the central angle in radians
Application of relation between arc of length and central angle?
The relation between the arc of length and the central angle is that the arc of length divided by one of the sides is the central angle in radians. If the arc is a full circle, then the central angle is 2pi radians or 360 degrees.
What is principle sine function?
It is sine defined between -pi/2 and + pi/2 radians (-90 deg and +90 deg) and its inverse is defined over this range.
What is the relationship between frequency measured in Hz and angle measured in radians?
First of all, frequency and angle have different physical dimensions. 'Frequency' has a reciprocal time in it ... "per second" ... and angle doesn't. The relationship you really want is the one between frequency and angular frequency ... "revolutions per second" and "radians per second". 1 revolution = 2 pi radians 1 revolution per second = 2 pi radians per second 1 revolution per year = 2 pi radians per year Angular frequency in radians per second = (2 pi) times (plain old frequency in Hz)
What does a zero with a horizontal line through it mean?
It means a central angle measured in radians. ex. Convert 360 degrees radians. 180 degrees = pi radians so 360 degrees = pi radians/180 degrees = 360pi radians/180 = 2 pi radians
A central angle of a circle of radius 30 cm intercepts an arc of 6 cm Express the central angle in radians and in degrees?
A central angle is measured by its intercepted arc. Let's denote the length of the intercepted arc with s, and the length of the radius r. So, s = 6 cm and r = 30 cm. When a central angle intercepts an arc whose length measure equals the length measure of the radius of the circle, this central angle has a measure 1 radian. To find the angle in our problem we use the following relationship: measure of an angle in radians = (length of the intercepted arc)/(length of the radius) measure of our angle = s/r = 6/30 = 1/5 radians. Now, we need to convert this measure angle in radians to degrees. Since pi radians = 180 degrees, then 1 radians = 180/pi degrees, so: 1/5 radians = (1/5)(180/pi) degrees = 36/pi degrees, or approximate to 11.5 degrees.
What is the measure of the central angle of a circle with the arc length of 29.21 and the circumference of 40.44?
arc length/circumference = central angle/2*pi (radians) So, central angle = 2*pi*arc length/circumference = 4.54 radians. Or, since 2*pi radians = 360 degrees, central angle = 360*arc length/circumference = 260.0 degrees, approx.
What is the relationship between radian and degrees?
simple: consider a circle. A circle is a point rotated through 360o. This rotation is also referred to as a rotation through 2Pi radians. Therefore we can make the following statements about the two forms of angular measurement 2 Pi radians = 360o 2 radians = 360o/Pi; 1 radian = 180o/Pi 1o = Pi radians/180
Is tangent ever undefined?
Yes. the tangents of odd multiples of pi/2 radians are not defined.
Deg per sec to rad per sec?
If you are asking for the conversion formulas, then think of the relationship between degress and radians. 360 degress = 2*pi radians, thus to convert every degree to radians, we divide both sides of the equation by 360. 1 degree = 2*pi/360 radians = pi/180 radians. thus to convert degrees into radians, just multiply the number of degrees to pi/180, where pi = 3.141592... by the way, the per sec appended on the unit does not matter in the conversion since both units are in per sec anyway
How do you find the arc length formed by a central angle x?
The arc length is equal to the angle times the radius. This assumes the angle is expressed in radians; if it isn't, convert it to radians first, or incorporate the conversion (usually from degrees to radians) in to your formula.
What is Relation between the length of the circular arc and the radian measures of its central angle?
You can think of an arc as a fraction of the circumferance of a circle. Also, a complete circle is 2pi radians, so any central angle is THETA / 2pi of a complete circle. Multiply by the circumferance to get the length of the arc: THETA / 2pi * 2(pi)(r) = THETA * r or the length of the arc is simply the radius times the central angle in radians
When is secant not defined?
The secant of an angle is the reciprocal of the cosine of the angle. So the secant is not defined whenever the cosine is zero That is, whenever the angle is a multiple of 180 degrees (or pi radians).
