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Trigonometry > Inverse Trigonometric Functions
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QuickNotes™  

Inverse Trigonometric Functions

Main definitions:

  • The secant function is defined by
    secθ = 1

    cosθ
    for values of θ where cosθ ≠ 0. (For values of θ where cosθ = 0, the secant is undefined.)
  • The cosecant function is defined by
    cscθ = 1

    sinθ
    for values of θ where sinθ ≠ 0. (For values of θ where sinθ = 0, the cosecant is undefined.)

Example 1:

Draw a graph of the secant function. Label all zeroes, maxes, mins, and asymptotes. What is the period of the secant function?

Example 2:

Find the values of secant and cosecant at the common angles in the first quadrant: 0, (π/6), (π /4),)(π/3), (π/2). Determine in which other quadrants the secant and cosecant are positive.

Example 3:

Determine if the secant and cosecant functions are odd, even, or neither.

Example 4:

Draw a graph of the cosecant function. Label all zeroes, maxes, mins, and asymptotes. What is the period of the cosecant function?

Example 5:

Find the secants and cosecants of (5π/6)R, 240° , and (7π/4)R.
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