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Reciprocal Trigonometric Functions on the Unit Circle quiz

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  • What is the definition of the cosecant function in terms of sine?
    Cosecant is defined as 1 divided by the sine of an angle.
  • How do you find the cosecant of an angle using the unit circle?
    You take 1 divided by the y-value at that angle on the unit circle.
  • What is the definition of the secant function in terms of cosine?
    Secant is defined as 1 divided by the cosine of an angle.
  • How do you find the secant of an angle using the unit circle?
    You take 1 divided by the x-value at that angle on the unit circle.
  • What is the definition of the cotangent function in terms of tangent?
    Cotangent is defined as 1 divided by the tangent of an angle.
  • How do you find the cotangent of an angle using the unit circle?
    You divide the x-value by the y-value at that angle on the unit circle.
  • What is the value of the cosecant of π/6?
    The cosecant of π/6 is 2.
  • What is the value of the cotangent of π/4?
    The cotangent of π/4 is 1.
  • What is the value of the secant of 0?
    The secant of 0 is 1.
  • If the sine of an angle is 1/2, what is its cosecant?
    The cosecant is 2, since 1 divided by 1/2 equals 2.
  • If the x and y values at an angle are equal, what is the cotangent of that angle?
    The cotangent is 1, because x divided by y equals 1.
  • Why are cosecant, secant, and cotangent called reciprocal functions?
    They are each the reciprocal of sine, cosine, and tangent, respectively.
  • How can you use the unit circle to find reciprocal trig functions without memorizing new values?
    You use the existing x and y values on the unit circle and apply the reciprocal definitions.
  • What is the formula for cotangent in terms of x and y on the unit circle?
    Cotangent is x divided by y.
  • What is the relationship between the secant function and the x-coordinate on the unit circle?
    Secant is the reciprocal of the x-coordinate, or 1/x.