0
There are always two angles between two radii of the same circle ... starting at one of them
and going each direction to the other one.
If you define the angle between them as the smaller of the two angles, then it can be anything
between 0° and 180°.
If you define it as the larger of the two, then it can be anything between 180° and 360°.
If you don't care which of the two angles is measured, then it can be anything between 0° and 360°.
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All radii have the same measure?
Yes in a particular circle
Relationship between degree of measure of a central angle and the arc it intercepts?
Arc length is equal to radius times the angle the arc subtends (makes) at the centre of the circle, but the angle needs to be in radians. Set your calculator to radians instead of degrees, or, to change degrees to radians, divide by 180 and times pi. The formula comes from the fact that the length of the arc is proportional to the circumference of the circle in the same ratio as the angle at the centre is to the complete revolution at the centre, so length of arc: circumference of circle = angle size : 360o arc/(2*pi*r) = angle in degrees/360 or angle in radians/(2*pi) so arc length is angle in degrees divided by 360, times the circumference of the circle. Answer will be in the same measurement unit as the radius.
What is the central angle of a circle with a diameter of 20 inches and divided into 20 congruent sectors?
1
Does a trigonometry tangent relate to a circle's tangent?
A circle's tangent is exactly the same as a triangle's tangent. If you look at a circle, you can make the radius the hypotenuse. Then make a vertical line from the point, and a horizontal line from the center. If you look, you have a triangle made inside the circle. This is why angles can be measured in radians, a unit that is derived from the circumference of a circle.-------------------------------------------------------------------------------------------By doing a little calculus, we find that the slope of the equation of a circle-the slope of the tangent line-is given by the tangent of an angle.AnswerEverything written above is correct, but doesn't have anything to do with tangents (in the circle sense of the word). Suppose you're given an angle theta. Draw a circle together with two radii, one horizontal and the other at an angle theta from the first one. (So far, this is the same as above.) Now draw the tangent to the circle at X, the point where the non-horizontal radius meets the circumference. Let Y be the point where this tangent meets the horizontal line through the centre. Then, assuming the radius is 1, tan(theta) is the distance XY, which is the length of part of the tangent.
Why does cos negative theta equal cos postitive theta?
The cosine is simply the x-coordinate of the unitary circle. It helps to draw the circle, and the sine and cosine (x and y coordinates), to visualize this. The y-coordinate is the same for a positive angle and for the corresponding negative angle.
