Evaluating inverse trigonometric functions

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Intros
Lessons
  1. Application of the Cancellation Laws

    Introduction to Evaluating Inverse Trigonometric Functions

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Examples
Lessons
  1. Understanding the Use of Inverse Trigonometric Functions

    Find the angles for each of the following diagrams.

    1. Evaluating inverse trigonometric functions
    2. Evaluating inverse trigonometric functions

  2. Find the angle for the following isosceles triangle.

    Evaluating inverse trigonometric functions
    1. Determining the Angles in Exact Values by Using Special Triangles

      Find the angles for each of the following diagrams in exact value.

      1. Evaluating inverse trigonometric functions
      2. Evaluating inverse trigonometric functions
    2. Application of the Cancellation Laws

      Solve the following inverse trigonometric functions:

      1. sin⁡(sin⁡−10.5)\sin (\sin^{-1} 0.5)
      2. cos⁡−1(cos⁡π4)\cos^{-1} (\cos \frac{\pi}{4})
      3. sin⁡−1(sin⁡3π4)\sin^{-1} (\sin \frac{3\pi}{4})
    3. Solving Expressions With One Inverse Trigonometry

      Solve the following inverse trigonometric functions:

      1. cos⁡−112\cos^{-1} \frac{1}{2}
      2. sin⁡−112\sin^{-1} \frac{1}{2}
    4. Evaluating Expressions With a Combination of Inverse and Non-Inverse Trigonometry

      Solve the following inverse trigonometric functions:

      1. sin⁡(cos⁡−132)\sin (\cos^{-1} \frac{\sqrt 3}{2})
      2. cos⁡(sin⁡−123)\cos (\sin^{-1} \frac{2}{3})
      3. cos⁡(2tan⁡−12)\cos (2\tan^{-1} \sqrt 2)
      4. cos⁡(sin⁡−1x)\cos (\sin^{-1} x)
    5. Special Cases: Evaluating Functions With Numbers Outside of the Restrictions

      Solve the following inverse trigonometric functions:

      1. cos⁡−1(cos⁡3π2)\cos^{-1} (\cos \frac{3\pi}{2})
      2. sin⁡−1(sin⁡5π2)\sin^{-1} (\sin \frac{5\pi}{2})
    Topic Notes
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    In this lesson, we will learn:

    • Application of the Cancellation Laws
    • Solving Expressions With One Inverse Trigonometry
    • Evaluating Expressions With a Combination of Inverse and Non-Inverse Trigonometry
    • Special Cases: Evaluating Functions With Numbers Outside of the Restrictions

    Cancellation Laws:

    sin⁡−1(sin⁡x)=x  \sin^{-1} (\sin x) = x\;, −π2≤x≤π2-\frac{\pi}{2} \leq x \leq \frac{\pi}{2}

    sin⁡(sin⁡−1x)=x  \sin (\sin^{-1} x) = x\;, −1≤x≤1-1 \leq x \leq 1

    cos⁡−1(cos⁡x)=x  \cos^{-1} (\cos x) = x\;, 0≤x≤π0 \leq x \leq \pi

    cos⁡(cos⁡−1x)=x  \cos (\cos^{-1} x) = x\;, −1≤x≤1-1 \leq x \leq 1

    tan⁡−1(tan⁡x)=x  \tan^{-1} (\tan x) = x\;, −π2≤x≤π2-\frac{\pi}{2} \leq x \leq \frac{\pi}{2}

    tan⁡(tan⁡−1x)=x  \tan (\tan^{-1} x) = x\;, −∞-\infty < xx < ∞\infty

    Trigonometric Identity:

    cos⁡2θ=cos⁡2θ−sin⁡2θ\cos 2\theta = \cos^{2} \theta - \sin^{2} \theta

    Basic Concepts
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    Related Concepts
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