M1410401

# M1410401 - 4.01 CHAPTER 4 TRIGONOMETRY(INTRO SECTION...

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4.01 CHAPTER 4: TRIGONOMETRY (INTRO) SECTION 4.1: (ANGLES); RADIAN AND DEGREE MEASURE PART A: ANGLES An angle is determined by rotating a ray (a “half-line”) from an initial side to a terminal side about its endpoint, called the vertex . A positive angle is determined by rotating the ray counterclockwise . A negative angle is determined by rotating the ray clockwise . A standard angle in standard position has the positive x -axis as its initial side and the origin as its vertex: Angles are often denoted by capital letters (with maybe the symbol) and by Greek letters such as θ (theta), φ (phi), α (alpha), β (beta),and γ (gamma) .

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4.02 PART B: DEGREE MEASURE FOR ANGLES We often associate angles with their rotational measures. There are 360 (360 degrees) in a full (counterclockwise) revolution. This is something of a cultural artifact; ancient Babylonians operated on a base-60 number system. We sometimes use DMS (Degree-Minute-Second) measure instead of decimal degrees. There are 60 minutes in 1 degree (Think: “hour”), and there are 60 seconds in 1 minute. For example, 34 3 0 2 ′′ 0 denotes 34 degrees, 30 minutes, and 20 seconds. PART C: RADIAN MEASURE FOR ANGLES Radian measure is more “mathematically natural,” and it is typically assumed in calculus. In fact, radian measure is assumed if there are no units present. Consider the unit circle (centered at the origin). 1 radian is defined to be the measure of a central angle (i.e., an angle whose vertex coincides with the center of the circle) that intercepts an arc length of 1 unit along the unit circle.
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M1410401 - 4.01 CHAPTER 4 TRIGONOMETRY(INTRO SECTION...

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