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Precalculus: Trigonometry Functions and Applications - Chapter 9

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Termini in questo insieme (20)

  • What is an angle in geometric terms?
    An angle is formed by rotating a ray, called the initial side, around its endpoint (the vertex) to a terminal side.
  • Define a line segment and a ray.
    A line segment AB is the portion of a line between points A and B. A ray AB starts at point A and extends infinitely through point B.
  • How many degrees are in one full rotation?
    There are 360° in one full rotation.
  • Classify angles by their degree measures.
    An acute angle is between 0° and 90°, a right angle is exactly 90°, an obtuse angle is between 90° and 180°, and a straight angle is exactly 180°.
  • What are complementary and supplementary angles?
    Two angles are complementary if their sum is 90°, and supplementary if their sum is 180°.
  • How many minutes and seconds are in one degree?
    One degree has 60 minutes (1' = 1/60°), and one minute has 60 seconds (1" = 1/60').
  • How do you convert degrees, minutes, and seconds to decimal degrees?
    Decimal degrees = degrees + (minutes/60) + (seconds/3600).
  • What are quadrantal angles?
    Angles in standard position with terminal sides on the x- or y-axis, such as 90°, 180°, 270°, and 360°.
  • Define coterminal angles.
    Angles with the same initial and terminal sides but differing by multiples of 360°.
  • How to find the smallest positive coterminal angle for 908°?
    Subtract multiples of 360°: 908° - 2(360°) = 188°.
  • What is a radian?
    A radian is the measure of an angle whose arc length equals the radius of the circle.
  • How many radians are in 360°?
    360° equals \(2\pi\) radians.
  • How to convert degrees to radians?
    Multiply degrees by \(\frac{\pi}{180}\).
  • How to convert radians to degrees?
    Multiply radians by \(\frac{180}{\pi}\).
  • Formula for arc length of a circle segment
    Arc length s = radius r × central angle θ in radians: \(s = r\theta\).
  • How to find the distance between two latitudes on Earth?
    Find the central angle between latitudes, convert to radians, then use distance = radius × angle.
  • Formula for the area of a sector of a circle
    Area = 1/2 × radius squared × central angle in radians: \(A = \frac{1}{2} r^2 \theta\).
  • Define angular speed and linear speed.
    Angular speed is the rate of change of the angle in radians per unit time. Linear speed is the distance traveled along the circle per unit time.
  • Relationship between linear speed and angular speed
    Linear speed v = radius r × angular speed ω: \(v = r\omega\).
  • How to find angular speed in radians per second from revolutions per minute?
    Multiply revolutions per minute by \(2\pi\) and divide by 60.