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    • ▾Trigonometry
      • ▸Angle measures and circles
        • •Intro to radians
        • •Arc length and sector formulas
        • •Converting between radians and degrees
        • •Degrees-minutes-seconds
      • ▸Right triangles and trig
        • •Intro to trigonometry
        • •Intro to the six basic trig functions
        • •Evaluating the six basic trig functions
        • •Evaluate the remaining basic trig functions
        • •Reciprocal and quotient identities
        • •Cofunction identities
        • •Special right triangles
        • •Area of an equilateral triangle
        • •Solving right triangles
        • •Circumradii of equilateral and isosceles triangles
      • ▸Graphing trig functions
        • •Graphing sin and cos
        • •Graphing tan and cot
        • •Graphing sec and csc
      • ▸Unit circle
        • •Finding the point on the unit circle
        • •Evaluating trig functions and solving trig equations using the unit circle
        • •Evaluating trig functions using coterminal and reference angles
        • •Proofs using the unit circle
        • •Signs of trig functions
      • ▾Inverse trig functions
        • •Composition of trig functions
        • •Evaluating inverse trig functions using the unit circle
        • •Evaluating inverse trig functions using a calculator
        • •Find the inverse of a trigonometric function
        • •Graphing inverse trigonometric functions
      • ▸Non-right triangles and trig
        • •Sine rule for area of a triangle
        • •Area of a segment
        • •Heron's formula
        • •Law of cosines
        • •Parallelogram law
        • •Stewart's theorem
        • •Law of sines
        • •Bretschneider's formula, and Brahmagupta's
      • ▸Trigonometric identities
        • •Double and half angle formulas
        • ▸Solving trig equations
          • •Solving trigonometric equations by graphing
          • •Solving trigonometric equations by factoring out the GCD
          • •Finding general solutions to trig equations
          • •Solving harder trig equations by factoring
          • •Solving trigonometric equations quadratic in form
          • •t-results
        • •Solving trig equations by factoring trinomials
        • •Sum and difference formulas
        • •Auxiliary angle method
        • •Finding the acute angle between two lines
        • •Product-to-sum and sum-to-product formulas
        • •Proving inverse trig identities
        • •Power reducing trig identities
        • •Pythagorean identities
        • •Disproving trigonometric identities by counterexample
        • •Even-odd trig identities
      • ▸Polar coordinates
        • •Plotting polar points
        • •Graphing polar equations
        • •Converting between polar and Cartesian form
      • ▸Complex numbers in polar form
        • •Multiplying and dividing complex numbers in polar form
        • •Proving de Moivre's theorem
        • •Powers of complex numbers using De Moivre's theorem
        • •Roots of complex numbers using De Moivre's theorem
      • ▸Hyperbolic and inverse hyperbolic functions
        • •Proving inverse hyperbolic identities
        • •Intro to hyperbolic functions
        • •Proving hyperbolic identities
        • •Solving hyperbolic equations
     › Trigonometry › Inverse trig functions

    Evaluating inverse trig functions using the unit circle

    Students will learn how to evaluate inverse trig functions using the unit circle. For example, evaluate \(\sin^{-1}(1/2).\)

    Conclude by giving your students these challenges:

    • Triangles Within Pentagons by NRICH
    • The Clockmaker's Birthday Cake by NRICH
    • Partitioning Revisited by NRICH
    • Sending a Parcel by NRICH
    • 2000 AMC 8, Problem 17

    Lessons and practice problems