Basic Inverse Trigonometric Functions

Key Questions

  • What are the Basic Inverse Trigonometric Functions?

    The basic inverse trigonometric functions are used to find the missing angles in right triangles. While the regular trigonometric functions are used to determine the missing sides of right angled triangles, using the following formulae:

    sin theta = opposite dividehypotenuse
    cos theta = adjacent divide hypotenuse
    tan theta = opposite divide adjacent

    the inverse trigonometric functions are used to find the missing angles, and can be used in the following way:

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    For example, to find angle A, the equation used is:

    cos^-1 = side b divide side c

    Callum S. · 1 · Feb 2 2015
  • How do you use inverse trig functions to solve equations?

    sinx=n if and only if x=arcsinn + 2 pi k for some integer k

    or x=(pi-arcsinn) + 2 pi k for some integer k

    cosx=n if and only if x=arccosn + 2 pi k for some integer k

    or x=(pi+arccosn) + 2 pi k for some integer k

    tanx=n if and only if x=arctan n + pi k for some integer k

    and so on.

    So,: Solve 7sinx-5 = 0

    7sinx-5 = 0
    7sinx = 5
    sinx = 5/7

    x=arcsin(5/7) +2 pi k for integer k
    or (pi-arcsin(5/7)) +2 pi k for integer k

    Jim H · 2 · Apr 12 2015
  • How do you use inverse trig functions to find angles?
    1. Know that arccos, arcsec functions are restricted to quad 1 and 2
    2. Know that arctan, arccot, arcsin, arccsc are restricted to quad 1 and 4
    3. And when you go to quadrant 4 with arctan, arccot, arcsin, arccsc, use negative angles

    Examples
    1.arcsin(1)= pi/2
    2. arctan(-1)= -pi/4
    3. arcsec(1/2)= DNE
    4. arc csc (-sqrt2)= -pi/4

    Hriman · · Mar 14 2018

Questions

Inverse Trigonometric Functions