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Precalculus: Angles, Radian Measure, and Trigonometric Functions

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Termini in questo insieme (20)

  • What is an acute angle?
    An acute angle is an angle less than 90 degrees (< 90°).
  • Define a right angle.
    A right angle measures exactly 90 degrees (1/4 rotation).
  • What is an obtuse angle?
    An obtuse angle is an angle greater than 90 degrees but less than 180 degrees (90° < θ < 180°).
  • What is a straight angle?
    A straight angle measures exactly 180 degrees (1/2 rotation).
  • How do you convert degrees to radians?
    Multiply degrees by \(\frac{\pi\text{ radians}}{180^\circ}\).
  • How do you convert radians to degrees?
    Multiply radians by \(\frac{180^\circ}{\pi\text{ radians}}\).
  • What is the formula for arc length?
    Arc length s is given by \(s = r\theta\), where r is radius and θ is angle in radians.
  • What is a coterminal angle?
    Two angles with the same initial and terminal sides but different rotations are called coterminal angles.
  • Define linear speed in circular motion.
    Linear speed v is \(v = \frac{s}{t}\), where s is arc length and t is time.
  • Define angular speed in circular motion.
    Angular speed ω is \(\omega = \frac{\theta}{t}\), where θ is angle in radians and t is time.
  • How is linear speed related to angular speed?
    Linear speed v is related to angular speed ω by \(v = r\omega\), where r is radius.
  • What is the domain and range of sine and cosine functions?
    Domain: all real numbers (-∞, ∞). Range: [-1, 1].
  • Which trigonometric functions are even and which are odd?
    Cosine and secant are even. Sine, cosecant, tangent, and cotangent are odd.
  • State the quotient identities for tangent and cotangent.
    \(\tan t = \frac{\sin t}{\cos t}\) and \(\cot t = \frac{\cos t}{\sin t}\).
  • What defines a periodic function?
    A function f is periodic if there exists a positive number p such that f(t + p) = f(t) for all t.
  • What is the period of sine and cosine functions?
    The sine and cosine functions have a period of \(2\pi\).
  • What is the period of tangent and cotangent functions?
    The tangent and cotangent functions have a period of \(\pi\).
  • State the Pythagorean identity involving sine and cosine.
    \(\sin^2 t + \cos^2 t = 1\).
  • State the Pythagorean identity involving tangent and secant.
    \(\tan^2 t + 1 = \sec^2 t\).
  • State the Pythagorean identity involving cotangent and cosecant.
    \(1 + \cot^2 t = \csc^2 t\).