Abstract
This chapter focuses on the angles and triangles in applied mathematics. An angle is the result of rotating a half line about its end point. It is said to be positive if the rotation is counterclockwise and negative if the rotation is clockwise. Angles are measured in two basic ways: (1) in degrees, a degree being ▪ of a complete revolution; and (2) in radians, a radian being ▪ of a complete revolution. The circumference of a unit circle is 2π, so it can be seen that the radian measure is a measure of the arc an angle intercepts. The reference angle θ' of an angle θ is the acute angle formed by the terminal side of θ and the x-axis. If an angle θ subtends an arc of length s in a circle of radius r, then the radian measure of θ = s/r. The reference angle concept allows the application of only acute angles when finding the trigonometric values of any angle. The trigonometric functions of acute angles can be defined in terms of the sides of a right triangle. Right triangle trigonometry can be used to solve many practical problems in areas as diverse as carpentry and navigation.
Published Version
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