You are watching: For a particular angle theta the cosine function
Formulas because that arcs and also sectors the circlesYou can easily find both the size of an arc and also the area the a sector for an angle θ in a circle of radius r.
|Length of an arc. The length of the arc is just the radius r time the edge θ where the angle is measure up in radians. To convert from levels to radians, multiply the variety of degrees by π/180.|
|Area of a sector. The area the the sector is half the square of the radius times the angle, where, again, the edge is measure up in radians.|
|Half the basic times the height. This is the usual one to use because it’s simplest and also you usually have that information. Choose any side to call the base b. Then if h is the distance from opposing vertex come b, climate the area is half of bh.|
|Heron’s formula. This is beneficial when you know the three sides a, b, and c of the triangle, and also all you desire to recognize is the area. Permit s be half their sum, dubbed the semiperimeter. Climate the area is the square root of the product of s, s−a, s−b, and also s−c.|
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use this once you recognize two sides, a and b, and the had angle, C. The area is half the product the the 2 sides time the sine the the contained angle.